observer.rar

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该文章中描述了系统辨识与自适应控制的结合,比较系统跟全面
observer.rar
内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/622b83433d2fbb00079bc7ca/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622b83433d2fbb00079bc7ca/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">A<span class="_ _0"> </span><span class="ls1">State<span class="_ _0"> </span><span class="ls2">Obser<span class="ls3">v<span class="_ _1"></span><span class="ls4">er<span class="_ _0"> </span><span class="ls5">f<span class="_ _1"></span><span class="ls4">or<span class="_ _0"> </span><span class="ls6">L<span class="_ _2"></span><span class="ls7">TI<span class="_ _0"> </span><span class="ls8">Systems<span class="_ _0"> </span><span class="ls9">with<span class="_ _0"> </span><span class="lsa">Delay<span class="ls3">ed<span class="_ _0"> </span><span class="lsb">Outputs:<span class="_ _0"> </span><span class="ls6">T<span class="_ _1"></span><span class="lsc">ime-V<span class="_ _2"></span><span class="lsd">arying</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 lsa ws0">Delay</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 lse ws0">Kamesh<span class="_ _3"> </span><span class="lsf">Subbarao</span></div><div class="t m0 x4 h3 y4 ff2 fs1 fc0 sc0 ls10 ws0">Assistant<span class="_ _3"> </span><span class="ls11">Professor</span></div><div class="t m0 x5 h3 y5 ff2 fs1 fc0 sc0 ls12 ws0">Dept.<span class="_ _3"> </span><span class="ls13">of<span class="_ _3"> </span><span class="ls14">Mechanical<span class="_ _3"> </span><span class="ls15">&amp;<span class="_ _3"> </span><span class="ls16">Aerospace<span class="_ _3"> </span><span class="ls17">Engg.</span></span></span></span></span></div><div class="t m0 x6 h3 y6 ff2 fs1 fc0 sc0 ls18 ws0">Uni<span class="_ _1"></span><span class="ls19">v<span class="_ _4"></span><span class="ls1a">.<span class="_ _3"> </span><span class="ls13">of<span class="_ _3"> </span><span class="ls1b">T<span class="_ _4"></span><span class="ls1c">e<span class="ls1d">xas<span class="_ _3"> </span><span class="ls1e">at<span class="_ _3"> </span><span class="ls1f">Arlington</span></span></span></span></span></span></span></span></div><div class="t m0 x6 h3 y7 ff2 fs1 fc0 sc0 ls20 ws0">Arlington,<span class="_ _3"> </span><span class="ls21">TX<span class="_ _3"> </span><span class="ls22">76019,<span class="_ _3"> </span><span class="ls23">USA</span></span></span></div><div class="t m0 x4 h4 y8 ff3 fs2 fc0 sc0 ls24 ws0">subbarao@uta.edu</div><div class="t m0 x7 h3 y9 ff2 fs1 fc0 sc0 ls25 ws0">Pra<span class="ls19">v<span class="_ _1"></span><span class="ls26">een<span class="_ _3"> </span><span class="ls27">C.<span class="_ _3"> </span><span class="ls28">Muralidhar</span></span></span></span></div><div class="t m0 x8 h3 ya ff2 fs1 fc0 sc0 ls29 ws0">Graduate<span class="_ _3"> </span><span class="ls2a">Student</span></div><div class="t m0 x9 h3 yb ff2 fs1 fc0 sc0 ls2b ws0">Department<span class="_ _3"> </span><span class="ls13">of<span class="_ _3"> </span><span class="ls2c">Electrical<span class="_ _3"> </span><span class="ls17">Engg.</span></span></span></div><div class="t m0 xa h3 yc ff2 fs1 fc0 sc0 ls18 ws0">Uni<span class="_ _1"></span><span class="ls19">v<span class="_ _4"></span><span class="ls1a">.<span class="_ _3"> </span><span class="ls13">of<span class="_ _3"> </span><span class="ls1b">T<span class="_ _4"></span><span class="ls1c">e<span class="ls1d">xas<span class="_ _3"> </span><span class="ls1e">at<span class="_ _3"> </span><span class="ls1f">Arlington</span></span></span></span></span></span></span></span></div><div class="t m0 xa h3 yd ff2 fs1 fc0 sc0 ls20 ws0">Arlington,<span class="_ _3"> </span><span class="ls21">TX<span class="_ _3"> </span><span class="ls22">76019,<span class="_ _3"> </span><span class="ls23">USA</span></span></span></div><div class="t m0 xb h4 ye ff3 fs2 fc0 sc0 ls24 ws0">pcm3824@exchange.uta.edu</div><div class="t m0 xc h5 yf ff4 fs2 fc0 sc0 ls2d ws0">Abstract<span class="ff1 ls2e">&#8212;<span class="_ _5"> </span><span class="ls2f">This<span class="_ _6"> </span><span class="ls30">paper<span class="_ _6"> </span><span class="ls31">analyzes<span class="_ _6"> </span><span class="ls32">the<span class="_ _6"> </span><span class="ls15">stability<span class="_ _6"> </span></span></span></span>pr<span class="ls29">operties<span class="_ _6"> </span><span class="ls33">of</span></span></span></span></span></div><div class="t m0 x1 h6 y10 ff1 fs2 fc0 sc0 ls30 ws0">a<span class="_ _6"> </span><span class="lse">state<span class="_ _6"> </span><span class="ls34">obser<span class="_ _1"></span><span class="ls30">v<span class="ls35">er<span class="_ _6"> </span><span class="ls36">estimating<span class="_ _7"> </span><span class="ls32">the<span class="_ _7"> </span><span class="ls4">system<span class="_ _6"> </span><span class="ls37">states<span class="_ _6"> </span><span class="ls38">fr<span class="ls39">om<span class="_ _7"> </span><span class="ls3a">delay</span></span></span></span></span></span></span></span>ed</span></span></span></div><div class="t m0 x1 h6 y11 ff1 fs2 fc0 sc0 ls3b ws0">measur<span class="ls3c">ements<span class="_ _3"> </span><span class="ls3d">f<span class="ls3e">or<span class="_ _3"> </span><span class="ls30">a<span class="_ _3"> </span><span class="ls3f">linear<span class="_ _8"> </span><span class="ls40">time<span class="_ _3"> </span><span class="ls41">in</span></span></span>v<span class="ls42">ariant<span class="_ _3"> </span><span class="ls43">plant.<span class="_ _3"> </span><span class="ls2d">The<span class="_ _8"> </span><span class="ls3a">delay<span class="_ _3"> </span><span class="ls44">is</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h6 y12 ff1 fs2 fc0 sc0 ls45 ws0">assumed<span class="_ _8"> </span><span class="ls33">to<span class="_ _8"> </span><span class="ls30">be<span class="_ _8"> </span>a<span class="_ _9"> </span><span class="ls46">kno<span class="ls47">wn<span class="_ _8"> </span><span class="ls48">piecewise<span class="_ _8"> </span><span class="ls31">constant<span class="_ _8"> </span><span class="ls49">function<span class="_ _8"> </span></span></span></span></span></span></span>of<span class="_ _9"> </span><span class="ls4a">time.</span></span></div><div class="t m0 x1 h6 y13 ff1 fs2 fc0 sc0 ls2d ws0">The<span class="_ _3"> </span><span class="ls34">obser<span class="ls30">v<span class="ls35">er<span class="_ _3"> </span><span class="ls4b">construction<span class="_ _3"> </span><span class="ls44">is<span class="_ _3"> </span></span></span></span>a<span class="_ _3"> </span><span class="ls4c">tw<span class="_ _1"></span><span class="ls30">o<span class="_ _3"> </span><span class="ls4d">step<span class="_ _3"> </span></span>pr<span class="ls27">ocedur<span class="_ _1"></span><span class="ls4e">e<span class="_ _3"> </span><span class="ls46">and<span class="_ _3"> </span><span class="ls4f">has<span class="_ _3"> </span><span class="ls30">a</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h6 y14 ff1 fs2 fc0 sc0 ls49 ws0">&#8220;chain-lik<span class="ls3e">e&#8221;<span class="_ _8"> </span><span class="ls50">structur<span class="ls51">e,<span class="_ _9"> </span><span class="ls52">consisting<span class="_ _9"> </span><span class="ls33">of<span class="_ _9"> </span><span class="ls4c">tw<span class="ls30">o<span class="_ _9"> </span><span class="ls53">cascaded<span class="_ _a"> </span><span class="ls54">dynamical</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h6 y15 ff1 fs2 fc0 sc0 ls55 ws0">systems.<span class="_ _b"> </span><span class="ls2d">The<span class="_ _b"> </span><span class="ls16">manifestation<span class="_ _b"> </span><span class="ls33">of<span class="_ _b"> </span><span class="ls32">the<span class="_ _b"> </span><span class="ls56">time-v<span class="ls57">arying<span class="_ _b"> </span><span class="ls3a">delay<span class="ls30">ed<span class="_ _b"> </span><span class="ls58">output</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h6 y16 ff1 fs2 fc0 sc0 ls59 ws0">on<span class="_ _c"> </span><span class="ls32">the<span class="_ _c"> </span><span class="ls34">obser<span class="ls30">v<span class="ls35">er<span class="_ _b"> </span><span class="ls15">stability<span class="_ _c"> </span><span class="ls44">is<span class="_ _c"> </span><span class="lsf">analyzed<span class="_ _c"> </span><span class="ls33">at<span class="_ _c"> </span><span class="ls5a">both<span class="_ _c"> </span></span></span></span></span></span></span></span></span>the<span class="_ _c"> </span><span class="ls5b">&#8220;zer<span class="ls5c">oth&#8221;<span class="_ _b"> </span><span class="ls46">and</span></span></span></span></div><div class="t m0 x1 h6 y17 ff1 fs2 fc0 sc0 ls32 ws0">the<span class="_ _b"> </span><span class="ls5d">&#8220;&#64257;rst&#8221;<span class="_ _c"> </span><span class="ls5e">links<span class="_ _b"> </span><span class="ls41">in<span class="_ _c"> </span></span></span></span>the<span class="_ _b"> </span><span class="ls5f">chain<span class="_ _c"> </span><span class="ls33">of<span class="_ _b"> </span><span class="ls34">obser<span class="ls30">v<span class="ls60">ers.</span></span></span></span></span></div><div class="t m0 xd h7 y18 ff2 fs3 fc0 sc0 ls61 ws0">I<span class="_ _d"></span><span class="ls62">.<span class="_ _6"> </span></span>I<span class="_ _d"></span><span class="fs4 ls63">N<span class="_ _d"></span><span class="ls64">T<span class="_ _d"></span><span class="ls65">R<span class="_ _d"></span></span></span>O<span class="_ _d"></span>D<span class="_ _d"></span>U<span class="_ _d"></span><span class="ls65">C<span class="_ _d"></span><span class="ls64">T<span class="_ _d"></span><span class="ls66">I<span class="_ _d"></span></span></span></span>O<span class="_ _d"></span>N</span></div><div class="t m0 x1 h7 y19 ff2 fs3 fc0 sc0 ls67 ws0">In<span class="_ _e"> </span>se<span class="ls68">v<span class="_ _1"></span><span class="ls3a">eral<span class="_ _e"> </span><span class="ls69">real-time<span class="_ _e"> </span><span class="ls6a">applications,<span class="_ _e"> </span><span class="ls36">all<span class="_ _e"> </span><span class="ls6b">the<span class="_ _e"> </span><span class="ls6c">state<span class="_ _e"> </span><span class="ls68">v<span class="_ _1"></span><span class="ls15">ariables</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y1a ff2 fs3 fc0 sc0 ls4b ws0">may<span class="_ _0"> </span><span class="ls6d">not<span class="_ _0"> </span><span class="ls6e">be<span class="_ _6"> </span><span class="ls6f">a<span class="ls68">v<span class="ls70">ailable<span class="_ _6"> </span><span class="ls71">for<span class="_ _0"> </span><span class="ls16">direct<span class="_ _0"> </span><span class="ls9">measurements.<span class="_ _0"> </span><span class="ls67">Hence<span class="_ _0"> </span></span></span></span></span></span></span>a</span></span></span></div><div class="t m0 x1 h7 y1b ff2 fs3 fc0 sc0 ls6c ws0">state<span class="_ _e"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _f"> </span><span class="ls73">is<span class="_ _f"> </span><span class="ls44">generally<span class="_ _e"> </span><span class="ls74">emplo<span class="ls75">yed<span class="_ _e"> </span><span class="ls76">to<span class="_ _f"> </span><span class="ls77">reconstruct<span class="_ _e"> </span><span class="ls6b">the</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y1c ff2 fs3 fc0 sc0 ls78 ws0">unmeasurable<span class="_ _10"> </span><span class="ls6c">state<span class="_ _10"> </span><span class="ls68">v<span class="ls79">ariables.<span class="_ _10"> </span><span class="ls7a">The<span class="_ _10"> </span><span class="ls72">observ<span class="_ _4"></span><span class="ls7b">ation<span class="_ _10"> </span><span class="ls7c">problem</span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y1d ff2 fs3 fc0 sc0 ls73 ws0">is<span class="_ _0"> </span><span class="ls63">complicated<span class="_ _0"> </span><span class="ls7d">if<span class="_ _0"> </span><span class="ls6b">the<span class="_ _0"> </span><span class="ls7e">system<span class="_ _0"> </span><span class="ls6d">output<span class="_ _0"> </span></span></span></span></span></span>is<span class="_ _0"> </span><span class="ls6f">a<span class="ls68">v<span class="ls70">ailable<span class="_ _0"> </span><span class="ls7f">after<span class="_ _0"> </span></span></span></span>a</span></div><div class="t m0 x1 h7 y1e ff2 fs3 fc0 sc0 ls80 ws0">delay<span class="_ _10"> </span><span class="ls81">interv<span class="ls1d">al.<span class="_ _10"> </span><span class="ls82">Studies<span class="_ _10"> </span><span class="ls6e">ha<span class="_ _1"></span><span class="ls68">v<span class="ls6f">e<span class="_ _10"> </span><span class="ls3d">sho<span class="_ _4"></span><span class="ls83">wn<span class="_ _10"> </span><span class="ls2d">that<span class="_ _10"> </span><span class="ls81">stable<span class="_ _11"> </span><span class="ls84">&#8220;time-</span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y1f ff2 fs3 fc0 sc0 ls85 ws0">delay&#8221;<span class="_ _8"> </span><span class="ls72">observ<span class="ls71">ers<span class="_ _3"> </span><span class="ls86">can<span class="_ _8"> </span><span class="ls6e">be<span class="_ _8"> </span><span class="ls87">realized<span class="_ _8"> </span><span class="ls76">in<span class="_ _3"> </span></span>practice<span class="_ _8"> </span><span class="ls6a">under<span class="_ _8"> </span><span class="ls88">suitable</span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y20 ff2 fs3 fc0 sc0 ls89 ws0">conditions<span class="_ _3"> </span><span class="ls1d">[1]-[4].<span class="_ _3"> </span><span class="ls34">Careful<span class="_ _c"> </span><span class="ls8a">scrutin<span class="ls68">y<span class="_ _3"> </span><span class="ls67">of<span class="_ _3"> </span><span class="ls8b">research<span class="_ _3"> </span><span class="ls8c">w<span class="ls72">ork<span class="_ _c"> </span><span class="ls5f">re</span></span></span></span></span>v<span class="ls71">eal</span></span></span></span></span></div><div class="t m0 x1 h7 y21 ff2 fs3 fc0 sc0 ls8d ws0">though<span class="_ _b"> </span><span class="ls2d">that<span class="_ _b"> </span><span class="ls39">while<span class="_ _b"> </span><span class="ls6b">the<span class="_ _12"> </span><span class="ls8e">delays<span class="_ _12"> </span><span class="ls44">associated<span class="_ _b"> </span><span class="ls8f">with<span class="_ _b"> </span><span class="ls7c">states<span class="_ _b"> </span><span class="ls15">[10]-[12]</span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y22 ff2 fs3 fc0 sc0 ls6e ws0">ha<span class="ls68">v<span class="_ _1"></span><span class="ls6f">e<span class="_ _b"> </span><span class="ls88">been<span class="_ _b"> </span><span class="ls90">studied<span class="_ _b"> </span><span class="ls76">in<span class="_ _b"> </span><span class="ls91">great<span class="_ _c"> </span><span class="ls92">detail,<span class="_ _b"> </span><span class="ls6b">the<span class="_ _b"> </span><span class="ls6a">setbacks<span class="_ _c"> </span><span class="ls75">due<span class="_ _b"> </span></span></span></span></span></span>to<span class="_ _b"> </span><span class="ls6d">output</span></span></span></span></span></span></div><div class="t m0 x1 h7 y23 ff2 fs3 fc0 sc0 ls80 ws0">delay<span class="_ _c"> </span><span class="ls93">rami&#64257;cations<span class="_ _c"> </span><span class="ls4d">are<span class="_ _c"> </span><span class="ls94">rarely<span class="_ _b"> </span><span class="ls95">addressed.</span></span></span></span></div><div class="t m0 x1 h7 y24 ff2 fs3 fc0 sc0 lsc ws0">Notable<span class="_ _9"> </span><span class="ls8b">research<span class="_ _a"> </span><span class="ls76">to<span class="_ _9"> </span><span class="ls96">estimate<span class="_ _a"> </span><span class="ls6b">the<span class="_ _a"> </span><span class="ls7c">states<span class="_ _9"> </span></span></span></span>in<span class="_ _a"> </span><span class="ls6b">the<span class="_ _9"> </span><span class="ls6e">presence<span class="_ _a"> </span><span class="ls67">of</span></span></span></span></span></div><div class="t m0 x1 h7 y25 ff2 fs3 fc0 sc0 ls2 ws0">delayed<span class="_ _a"> </span><span class="ls82">outputs<span class="_ _7"> </span><span class="ls97">include<span class="_ _7"> </span><span class="ls98">constant-g<span class="ls6b">ain<span class="_ _a"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _7"> </span><span class="ls99">design<span class="_ _a"> </span><span class="ls71">[9]</span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y26 ff2 fs3 fc0 sc0 ls75 ws0">and<span class="_ _a"> </span><span class="ls80">chain<span class="_ _7"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _a"> </span><span class="ls71">for<span class="_ _a"> </span><span class="ls9a">observing<span class="_ _7"> </span><span class="ls6b">the<span class="_ _a"> </span><span class="ls7c">states<span class="_ _7"> </span><span class="ls9b">from<span class="_ _a"> </span><span class="ls2">delayed</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y27 ff2 fs3 fc0 sc0 ls82 ws0">outputs<span class="_ _7"> </span><span class="ls1d">[6]-[8].<span class="_ _a"> </span><span class="ls67">In<span class="_ _7"> </span><span class="ls6b">the<span class="_ _7"> </span><span class="ls9c">latter<span class="ls62">,<span class="_ _a"> </span></span></span>the<span class="_ _7"> </span><span class="ls80">chain<span class="_ _7"> </span></span></span>of<span class="_ _a"> </span><span class="ls6c">state<span class="_ _7"> </span><span class="ls72">observ<span class="ls71">ers</span></span></span></span></span></div><div class="t m0 x1 h7 y28 ff2 fs3 fc0 sc0 ls9d ws0">reb<span class="ls76">uild<span class="_ _7"> </span><span class="ls6b">the<span class="_ _7"> </span><span class="ls1b">systems<span class="_ _6"> </span><span class="ls7c">states<span class="_ _7"> </span><span class="ls29">at<span class="_ _6"> </span><span class="ls9e">dif<span class="ls94">ferent<span class="_ _7"> </span><span class="ls87">time-delay<span class="_ _6"> </span><span class="ls2f">instants</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y29 ff2 fs3 fc0 sc0 ls6d ws0">within<span class="_ _8"> </span><span class="ls6b">the<span class="_ _8"> </span><span class="ls80">delay<span class="_ _3"> </span><span class="ls68">windo<span class="ls8c">w<span class="_ _4"></span><span class="ls62">.<span class="_ _8"> </span><span class="ls7a">The<span class="_ _8"> </span><span class="ls35">main<span class="_ _3"> </span><span class="ls9f">assumption<span class="_ _8"> </span><span class="ls73">is<span class="_ _8"> </span><span class="ls2d">that<span class="_ _8"> </span><span class="ls6b">the</span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y2a ff2 fs3 fc0 sc0 ls80 ws0">delay<span class="_ _8"> </span><span class="ls73">is<span class="_ _8"> </span><span class="lsa0">kno<span class="_ _1"></span><span class="ls83">wn<span class="_ _8"> </span><span class="ls75">and<span class="_ _8"> </span><span class="ls6f">a<span class="_ _8"> </span><span class="lsa1">constant.<span class="_ _3"> </span><span class="ls7d">It<span class="_ _8"> </span><span class="ls73">is<span class="_ _8"> </span><span class="lsa2">seen<span class="_ _8"> </span><span class="ls2d">that<span class="_ _8"> </span></span></span></span>if<span class="_ _8"> </span><span class="ls6b">the<span class="_ _8"> </span><span class="ls80">delay</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y2b ff2 fs3 fc0 sc0 ls73 ws0">is<span class="_ _8"> </span><span class="lsa0">kno<span class="ls83">wn<span class="_ _3"> </span><span class="ls68">b<span class="ls76">ut<span class="_ _8"> </span><span class="lsa3">time-v<span class="ls8e">arying<span class="_ _3"> </span><span class="ls6b">the<span class="_ _8"> </span><span class="ls72">observ<span class="ls7b">ation<span class="_ _8"> </span><span class="ls94">errors<span class="_ _8"> </span><span class="ls4d">are<span class="_ _8"> </span></span></span>quite</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y2c ff2 fs3 fc0 sc0 lsa4 ws0">lar<span class="ls87">ge.</span></div><div class="t m0 x1 h7 y2d ff2 fs3 fc0 sc0 ls67 ws0">In<span class="_ _6"> </span><span class="ls13">this<span class="_ _6"> </span><span class="lsa5">paper<span class="_ _1"></span><span class="ls62">,<span class="_ _6"> </span><span class="ls6b">the<span class="_ _6"> </span><span class="ls80">chain<span class="_ _6"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _7"> </span><span class="ls8f">with<span class="_ _6"> </span><span class="ls6f">a<span class="_ _6"> </span><span class="ls3b">cascade<span class="_ _6"> </span><span class="ls67">of<span class="_ _6"> </span><span class="ls68">two</span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y2e ff2 fs3 fc0 sc0 ls1b ws0">systems<span class="_ _b"> </span><span class="ls71">[6]<span class="_ _c"> </span><span class="lsa6">estimating<span class="_ _c"> </span><span class="ls6b">the<span class="_ _c"> </span><span class="ls7c">states<span class="_ _c"> </span><span class="ls9b">from<span class="_ _c"> </span></span></span>the<span class="_ _c"> </span><span class="ls2">delayed<span class="_ _c"> </span><span class="ls6d">output<span class="_ _c"> </span><span class="ls73">is</span></span></span></span></span></span></div><div class="t m0 x1 h7 y2f ff2 fs3 fc0 sc0 ls6b ws0">considered.<span class="_ _8"> </span><span class="ls7a">The<span class="_ _8"> </span><span class="ls80">delay<span class="_ _8"> </span><span class="ls73">is<span class="_ _8"> </span><span class="ls6e">modeled<span class="_ _8"> </span><span class="ls67">as<span class="_ _8"> </span><span class="ls6f">a<span class="_ _8"> </span><span class="ls15">piece<span class="lsa7">wise<span class="_ _3"> </span><span class="lsa1">constant.</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y30 ff2 fs3 fc0 sc0 lsa8 ws0">W<span class="_ _4"></span><span class="ls6f">e<span class="_ _9"> </span><span class="lsa9">analyze<span class="_ _7"> </span><span class="ls6b">the<span class="_ _a"> </span><span class="lsa">impact<span class="_ _a"> </span><span class="ls67">of<span class="_ _7"> </span></span></span>the<span class="_ _a"> </span><span class="lsaa">time<span class="_ _a"> </span><span class="ls68">v<span class="ls8e">arying<span class="_ _a"> </span></span></span></span></span>nature<span class="_ _a"> </span><span class="ls67">of<span class="_ _a"> </span><span class="ls6b">the</span></span></span></span></div><div class="t m0 x1 h7 y31 ff2 fs3 fc0 sc0 ls80 ws0">delay<span class="_ _b"> </span><span class="ls68">on<span class="_ _b"> </span><span class="ls6b">the<span class="_ _12"> </span><span class="ls98">stability<span class="_ _b"> </span><span class="ls67">of<span class="_ _b"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _b"> </span><span class="ls78">system.<span class="_ _b"> </span></span></span></span>In<span class="_ _b"> </span></span></span>the<span class="_ _12"> </span><span class="ls48">process,<span class="_ _b"> </span><span class="lsab">we</span></span></span></span></div><div class="t m0 x1 h7 y32 ff2 fs3 fc0 sc0 ls15 ws0">deri<span class="ls68">v<span class="_ _1"></span><span class="ls6f">e<span class="_ _9"> </span><span class="ls89">conditions<span class="_ _a"> </span><span class="ls6a">under<span class="_ _a"> </span><span class="lsac">which<span class="_ _9"> </span></span></span></span>e<span class="lsad">xponential<span class="_ _a"> </span><span class="ls98">stability<span class="_ _9"> </span><span class="ls67">of<span class="_ _a"> </span><span class="ls6b">the</span></span></span></span></span></span></div><div class="t m0 x1 h7 y33 ff2 fs3 fc0 sc0 ls72 ws0">observ<span class="ls5f">er<span class="_ _b"> </span><span class="ls1d">error<span class="_ _c"> </span><span class="ls44">dynamics<span class="_ _c"> </span><span class="ls73">is<span class="_ _c"> </span><span class="ls7c">guaranteed.</span></span></span></span></span></div><div class="t m0 x1 h7 y34 ff2 fs3 fc0 sc0 ls7a ws0">The<span class="_ _c"> </span><span class="lsa5">paper<span class="_ _3"> </span><span class="ls73">is<span class="_ _3"> </span><span class="ls67">or<span class="ls68">g<span class="ls85">anized<span class="_ _c"> </span></span></span>as<span class="_ _c"> </span><span class="ls8a">follo<span class="lsae">ws.<span class="_ _c"> </span></span></span>In<span class="_ _3"> </span><span class="lsaf">section<span class="_ _3"> </span><span class="ls2d">2,<span class="_ _c"> </span><span class="ls6b">the<span class="_ _3"> </span><span class="ls45">mathe-</span></span></span></span></span></span></span></div><div class="t m0 x1 h7 y35 ff2 fs3 fc0 sc0 ls4d ws0">matical<span class="_ _c"> </span><span class="ls2">description<span class="_ _3"> </span><span class="ls67">of<span class="_ _3"> </span><span class="ls6b">the<span class="_ _c"> </span><span class="ls9a">single-input<span class="_ _3"> </span><span class="lsb0">single-output<span class="_ _3"> </span><span class="lsb1">(SISO)</span></span></span></span></span></span></div><div class="t m0 x1 h7 y36 ff2 fs3 fc0 sc0 ls16 ws0">linear<span class="_ _12"> </span><span class="ls1b">systems<span class="_ _12"> </span><span class="ls8f">with<span class="_ _13"> </span><span class="ls2">delayed<span class="_ _13"> </span><span class="ls6d">output<span class="_ _12"> </span><span class="ls73">is<span class="_ _12"> </span><span class="lsb2">presented.<span class="_ _13"> </span><span class="ls67">In<span class="_ _12"> </span><span class="lsaf">section<span class="_ _12"> </span><span class="ls2d">3,</span></span></span></span></span></span></span></span></span></div><div class="t m0 xe h7 y37 ff2 fs3 fc0 sc0 ls6b ws0">the<span class="_ _3"> </span><span class="ls44">dynamics<span class="_ _3"> </span><span class="ls75">and<span class="_ _c"> </span></span></span>the<span class="_ _3"> </span><span class="ls98">stability<span class="_ _3"> </span><span class="lsb3">concepts<span class="_ _3"> </span><span class="ls67">of<span class="_ _3"> </span></span></span></span>the<span class="_ _3"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _c"> </span><span class="ls4d">are</span></span></span></div><div class="t m0 xe h7 y38 ff2 fs3 fc0 sc0 lsb4 ws0">discussed.<span class="_ _9"> </span><span class="ls67">In<span class="_ _a"> </span><span class="lsaf">section<span class="_ _a"> </span><span class="ls2d">4,<span class="_ _a"> </span><span class="ls6b">the<span class="_ _9"> </span><span class="ls48">theoretical<span class="_ _a"> </span><span class="lsb">results<span class="_ _a"> </span><span class="ls4d">are<span class="_ _a"> </span><span class="ls68">v<span class="ls8e">eri&#64257;ed</span></span></span></span></span></span></span></span></span></div><div class="t m0 xe h7 y39 ff2 fs3 fc0 sc0 lsb5 ws0">through<span class="_ _6"> </span><span class="lsb6">simulation<span class="_ _0"> </span><span class="lsb7">studies<span class="_ _6"> </span><span class="lsa">performed<span class="_ _6"> </span><span class="ls68">on<span class="_ _0"> </span><span class="ls6f">a<span class="_ _6"> </span><span class="lsb8">simple<span class="_ _0"> </span><span class="ls16">linear</span></span></span></span></span></span></span></div><div class="t m0 xe h7 y3a ff2 fs3 fc0 sc0 ls7e ws0">system<span class="_ _c"> </span><span class="ls75">and<span class="_ _c"> </span><span class="ls6d">&#64257;nally<span class="_ _c"> </span><span class="ls6b">the<span class="_ _b"> </span><span class="ls39">conclusions<span class="_ _c"> </span><span class="ls4d">are<span class="_ _c"> </span><span class="lsb2">presented.</span></span></span></span></span></span></div><div class="t m0 xf h7 y3b ff2 fs3 fc0 sc0 ls61 ws0">I<span class="_ _d"></span>I<span class="_ _d"></span><span class="ls62">.<span class="_ _6"> </span><span class="lsb9">L<span class="_ _d"></span><span class="fs4 ls66">I<span class="_ _d"></span><span class="ls63">N<span class="_ _d"></span><span class="ls64">E<span class="_ _d"></span></span>A<span class="_ _d"></span><span class="ls65">R<span class="_ _12"> </span><span class="ls89">S<span class="_ _d"></span></span></span>Y<span class="_ _d"></span><span class="ls89">S<span class="_ _14"></span><span class="ls64">T<span class="_ _d"></span>E<span class="_ _d"></span><span class="lsb9">M<span class="_ _d"></span></span></span>S<span class="_ _12"> </span>S<span class="_ _d"></span></span>U<span class="_ _d"></span><span class="ls65">B<span class="_ _d"></span><span class="lsba">J<span class="_ _d"></span><span class="ls64">E<span class="_ _d"></span></span></span>C<span class="_ _d"></span><span class="ls64">T<span class="_ _12"> </span>T<span class="_ _d"></span></span></span>O<span class="_ _12"> </span>O<span class="_ _d"></span>U<span class="_ _d"></span><span class="ls64">T<span class="_ _d"></span><span class="ls89">P<span class="_ _d"></span></span></span>U<span class="_ _d"></span><span class="ls64">T<span class="_ _12"> </span></span>D<span class="_ _14"></span><span class="ls64">E<span class="_ _d"></span>L<span class="_ _d"></span></span>A<span class="_ _1"></span>Y<span class="_ _d"></span><span class="ls89">S</span></span></span></span></span></div><div class="t m0 xe h7 y3c ff2 fs3 fc0 sc0 ls7a ws0">The<span class="_ _b"> </span><span class="ls78">class<span class="_ _c"> </span><span class="ls67">of<span class="_ _c"> </span><span class="lsb4">single-input-single-output<span class="_ _c"> </span><span class="lsb1">(SISO)<span class="_ _c"> </span><span class="ls1b">systems<span class="_ _b"> </span><span class="lsa2">con-</span></span></span></span></span></span></div><div class="t m0 xe h7 y3d ff2 fs3 fc0 sc0 ls44 ws0">sidered<span class="_ _c"> </span><span class="ls76">in<span class="_ _c"> </span><span class="ls13">this<span class="_ _c"> </span><span class="lsa5">paper<span class="_ _b"> </span><span class="ls4d">are<span class="_ _c"> </span><span class="ls92">represented<span class="_ _c"> </span><span class="lsbb">as,</span></span></span></span></span></span></div><div class="t m0 x10 h8 y3e ff5 fs3 fc0 sc0 lsbc ws0">&#729;</div><div class="t m0 x11 h8 y3f ff6 fs3 fc0 sc0 lsbd ws0">x<span class="ff5 lsbe">(<span class="ff7 lsbf">t</span>)<span class="_ _15"> </span><span class="lsc0">=<span class="_ _15"> </span></span></span><span class="lsc1">Ax<span class="ff5 lsbe">(<span class="ff7 lsbf">t</span>)<span class="_ _16"> </span><span class="lsc0">+<span class="_ _16"> </span></span></span><span class="lsc2">B<span class="_ _d"></span><span class="ff7 lsc3">u<span class="ff5 lsbe">(</span><span class="lsbf">t<span class="ff5 lsbe">)<span class="_ _15"> </span></span>t<span class="_ _13"> </span><span class="ff8 lsc0">&#8805;<span class="_ _12"> </span><span class="ff5 lsc4">&#8710;</span></span><span class="lsbc">,<span class="_ _17"> </span></span></span></span></span></span>x<span class="ff5 lsbe">(<span class="ff8 lsc0">&#8722;</span><span class="lsc4">&#8710;</span></span></div><div class="t m0 x12 h9 y40 ff9 fs5 fc0 sc0 lsc5 ws0">1</div><div class="t m0 x13 h8 y3f ff5 fs3 fc0 sc0 lsbe ws0">)<span class="_ _13"> </span><span class="lsc0">=</span></div><div class="t m0 x14 h8 y3e ff5 fs3 fc0 sc0 ls68 ws0">&#175;</div><div class="t m0 x15 ha y3f ff6 fs3 fc0 sc0 lsbd ws0">x</div><div class="t m0 x10 h8 y41 ff5 fs3 fc0 sc0 ls68 ws0">&#175;<span class="_ _18"></span><span class="ff7 lsc6">y<span class="_ _d"></span><span class="ff5 lsbe">(</span><span class="lsbf">t<span class="ff5 lsbe">)<span class="_ _15"> </span><span class="lsc0">=<span class="_ _15"> </span><span class="ff6 lsc7">C<span class="_ _d"></span><span class="lsbd">x</span></span></span>(</span>t<span class="_ _16"> </span><span class="ff8 lsc0">&#8722;<span class="_ _16"> </span><span class="ff5 ls27">&#8710;(</span></span>t<span class="ff5 lsc8">))<span class="_ _19"> </span><span class="ff2 ls71">(1)</span></span></span></span></div><div class="t m0 xe h8 y42 ff2 fs3 fc0 sc0 ls73 ws0">where<span class="_ _b"> </span><span class="ff6 lsbd">x<span class="ff5 lsbe">(<span class="ff7 lsbf">t</span>)<span class="_"> </span><span class="ff8 lsc9">&#8712;<span class="_ _b"> </span><span class="ffa lsca">R</span></span></span></span></div><div class="t m0 x16 hb y43 ffb fs5 fc0 sc0 lsab ws0">n</div><div class="t m0 x17 h8 y42 ff2 fs3 fc0 sc0 ls73 ws0">is<span class="_ _b"> </span><span class="ls6b">the<span class="_ _b"> </span><span class="ls6c">state<span class="_ _b"> </span><span class="ls68">v<span class="ls91">ector<span class="_ _4"></span><span class="ls62">.<span class="_ _b"> </span><span class="ff7 lsc3">u<span class="ff5 lsbe">(</span><span class="lsbf">t<span class="ff5 lsbe">)<span class="_"> </span><span class="ff8 lsc9">&#8712;<span class="_ _b"> </span><span class="ffa lsca">R<span class="_ _b"> </span></span></span></span></span></span><span class="ls73">is<span class="_ _b"> </span><span class="ls6b">the<span class="_ _b"> </span><span class="ls7e">system</span></span></span></span></span></span></span></span></div><div class="t m0 xe ha y44 ff2 fs3 fc0 sc0 lscb ws0">input.<span class="_ _0"> </span><span class="ff6 lscc">A<span class="_ _0"> </span></span><span class="ls75">and<span class="_ _0"> </span><span class="ff6 lsc2">B<span class="_ _e"> </span></span><span class="ls4d">are<span class="_ _0"> </span><span class="ls56">constant<span class="_ _0"> </span><span class="lscd">matrices<span class="_ _0"> </span><span class="ls8f">with<span class="_ _0"> </span><span class="lsce">appropriate</span></span></span></span></span></span></div><div class="t m0 xe h8 y45 ff2 fs3 fc0 sc0 ls8e ws0">dimensions.<span class="_ _0"> </span><span class="ff5 ls68">&#175;<span class="_ _18"></span><span class="ff7 lsc6">y<span class="_ _d"></span><span class="ff5 lsbe">(</span><span class="lsbf">t<span class="ff5 lsbe">)<span class="_ _7"> </span><span class="ff2 ls92">represents<span class="_ _6"> </span><span class="ls6b">the<span class="_ _6"> </span><span class="ls2">delayed<span class="_ _6"> </span><span class="ls6d">output<span class="_ _7"> </span><span class="ls39">while<span class="_ _6"> </span></span></span></span>the</span></span></span></span></span></span></div><div class="t m0 xe h8 y46 ff2 fs3 fc0 sc0 ls90 ws0">undelayed<span class="_ _c"> </span><span class="ls6d">output<span class="_ _c"> </span><span class="ls73">is<span class="_ _c"> </span><span class="ls92">represented<span class="_ _b"> </span><span class="ls67">as<span class="_ _c"> </span><span class="ff7 lsc6">y<span class="_ _d"></span><span class="ff5 lsbe">(</span><span class="lsbf">t<span class="ff5 lsbe">)<span class="_ _12"> </span><span class="lsc0">=<span class="_ _13"> </span><span class="ff6 lsc7">C<span class="_ _14"></span><span class="lsbd">x</span></span></span>(</span>t<span class="ff5 lsbe">)</span></span></span><span class="ls62">.</span></span></span></span></span></div><div class="t m0 xe h7 y47 ff2 fs3 fc0 sc0 ls7d ws0">It<span class="_ _1a"> </span><span class="ls73">is<span class="_ _1a"> </span><span class="ls6e">assumed<span class="_ _1a"> </span><span class="ls2d">that<span class="_ _1a"> </span><span class="ls6b">the<span class="_ _1a"> </span><span class="ls7e">system<span class="_ _1a"> </span><span class="ls76">in<span class="_ _1a"> </span><span class="ls71">(1)<span class="_ _1a"> </span></span></span></span></span></span></span>is<span class="_ _1a"> </span><span class="ls72">observ<span class="_ _1"></span><span class="ls67">able</span></span></span></div><div class="t m0 xe h8 y48 ff2 fs3 fc0 sc0 lscf ws0">i.e.,<span class="_ _10"> </span><span class="ls6b">the<span class="_ _1b"> </span><span class="ls15">pair<span class="_ _1b"> </span><span class="ff5 lsbe">(<span class="ff6 lscc">A<span class="ff7 lsbc">,<span class="_ _1c"> </span></span><span class="lsc7">C<span class="_ _d"></span></span></span>)<span class="_ _10"> </span></span><span class="ls73">is<span class="_ _1b"> </span><span class="lsd0">stabilizable.<span class="_ _10"> </span><span class="ls95">Alternately<span class="_ _4"></span><span class="ls62">,<span class="_ _1b"> </span><span class="ls91">there</span></span></span></span></span></span></span></div><div class="t m0 xe hc y49 ff2 fs3 fc0 sc0 ls6f ws0">e<span class="lsd1">xists<span class="_ _0"> </span></span>a<span class="_ _f"> </span><span class="ls90">suitably<span class="_ _f"> </span><span class="ls80">dimensioned<span class="_ _f"> </span><span class="ls68">g<span class="ls6b">ain<span class="_ _f"> </span><span class="lsa3">matrix<span class="_ _f"> </span><span class="ff7 lsd2">K<span class="_ _1b"> </span></span><span class="lsa7">such<span class="_ _f"> </span><span class="ls2d">that</span></span></span></span></span></span></span></div><div class="t m0 xe h8 y4a ff5 fs3 fc0 sc0 lsd3 ws0">Re<span class="_ _5"> </span><span class="lsbe">(<span class="ff7 lsd4">&#955;</span></span></div><div class="t m0 x18 hb y4b ffb fs5 fc0 sc0 ls4 ws0">i</div><div class="t m0 x19 h8 y4a ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff6 lscc">A<span class="_ _16"> </span><span class="ff8 lsc0">&#8722;<span class="_ _16"> </span></span><span class="lsd5">K<span class="_ _d"></span><span class="ff7 lsd6">C<span class="_ _14"></span></span></span></span><span class="lsc8">))<span class="_"> </span><span class="ff7 lsc0">&lt;<span class="_ _13"> </span></span><span class="ls68">0<span class="ff7 lsbc">,<span class="_ _6"> </span><span class="lsd7">i<span class="_"> </span></span></span><span class="lsc0">=<span class="_ _13"> </span></span>1<span class="ff7 lsbc">,<span class="_ _1c"> </span>.<span class="_ _5"> </span>.<span class="_ _5"> </span>.<span class="_ _1c"> </span>,<span class="_ _5"> </span><span class="lsd8">N<span class="_ _1d"> </span><span class="ff2 ls62">,<span class="_ _c"> </span><span class="ls73">where<span class="_ _c"> </span></span></span><span class="lsd4">&#955;</span></span></span></span></span></div><div class="t m0 x1a hb y4b ffb fs5 fc0 sc0 ls4 ws0">i</div><div class="t m0 x1b h8 y4a ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff8 lsbc">&#183;</span>)<span class="_ _c"> </span><span class="ff2 lsd1">denotes</span></div><div class="t m0 xe hc y4c ff2 fs3 fc0 sc0 ls6b ws0">the<span class="_ _c"> </span><span class="ff7 lsd7">i</span></div><div class="t m0 x1c h9 y4d ff9 fs5 fc0 sc0 lsa7 ws0">th</div><div class="t m0 x1d h8 y4c ff2 fs3 fc0 sc0 ls80 ws0">eigen<span class="_ _1"></span><span class="ls68">v<span class="_ _1"></span><span class="ls67">alue<span class="_ _b"> </span>of<span class="_ _c"> </span><span class="ff5 lsbe">(<span class="ff8 lsbc">&#183;</span>)</span><span class="ls62">.<span class="_ _c"> </span><span class="lsa8">W<span class="_ _4"></span><span class="ls6f">e<span class="_ _c"> </span><span class="lsd9">denote,<span class="_ _c"> </span><span class="ff6 lscc">A</span></span></span></span></span></span></span></div><div class="t m0 x1e hb y4e ffb fs5 fc0 sc0 lsda ws0">m</div><div class="t m0 x1f h8 y4c ff5 fs3 fc0 sc0 lsc0 ws0">=<span class="_ _13"> </span><span class="ff6 lscc">A<span class="_ _16"> </span></span><span class="ff8">&#8722;<span class="_ _16"> </span><span class="ff6 lsd5">K<span class="_ _14"></span><span class="ff7 lsd6">C<span class="_ _14"></span><span class="ff2 ls62">.</span></span></span></span></div><div class="t m0 xe h8 y4f ff5 fs3 fc0 sc0 lsc4 ws0">&#8710;<span class="_ _3"> </span><span class="ff2 ls73">is<span class="_ _3"> </span><span class="ls6f">a<span class="_ _3"> </span><span class="ls56">function<span class="_ _3"> </span><span class="ls67">of<span class="_ _3"> </span><span class="lsdb">time,<span class="_ _3"> </span><span class="lsdc">i.e,<span class="_ _3"> </span><span class="lsd9">its<span class="_ _3"> </span><span class="ls44">magnitude<span class="_ _3"> </span><span class="ls68">v<span class="ls2c">aries<span class="_ _c"> </span></span></span>randomly</span></span></span></span></span></span></span></span></div><div class="t m0 xe h8 y50 ff2 fs3 fc0 sc0 ls8f ws0">with<span class="_ _c"> </span><span class="lsaa">time<span class="_ _3"> </span><span class="ls75">and<span class="_ _c"> </span><span class="ff5 ls68">0<span class="_"> </span><span class="ff7 lsc0">&lt;<span class="_"> </span></span><span class="ls27">&#8710;(<span class="ff7 lsbf">t</span><span class="lsbe">)<span class="_ _12"> </span><span class="ff8 lsc0">&#8804;</span></span></span></span></span></span></div><div class="t m0 x20 h8 y51 ff5 fs3 fc0 sc0 ls68 ws0">&#732;</div><div class="t m0 x21 h8 y50 ff5 fs3 fc0 sc0 lsc4 ws0">&#8710;<span class="ff2 ls62">.</span></div><div class="t m0 x22 h8 y51 ff5 fs3 fc0 sc0 ls68 ws0">&#732;</div><div class="t m0 x23 h8 y50 ff5 fs3 fc0 sc0 lsc4 ws0">&#8710;<span class="_ _c"> </span><span class="ff2 ls73">is<span class="_ _3"> </span><span class="ls6b">the<span class="_ _c"> </span><span class="ls6a">upper<span class="_ _3"> </span><span class="ls68">bound<span class="_ _3"> </span>on<span class="_ _c"> </span><span class="ls36">all</span></span></span></span></span></div><div class="t m0 xe h7 y52 ff2 fs3 fc0 sc0 ls6b ws0">the<span class="_ _3"> </span><span class="lsdd">delays.<span class="_ _8"> </span><span class="ls7a">The<span class="_ _8"> </span><span class="ls6d">output<span class="_ _3"> </span><span class="ls80">delay<span class="_ _8"> </span><span class="ls73">is<span class="_ _3"> </span><span class="ls15">piece<span class="lsa7">wise<span class="_ _3"> </span><span class="lsa1">constant,<span class="_ _8"> </span><span class="lsdc">i.e,<span class="_ _8"> </span></span></span></span></span></span></span></span></span></span>the</div><div class="t m0 xe h8 y53 ff2 fs3 fc0 sc0 ls68 ws0">v<span class="ls67">alue<span class="_ _9"> </span><span class="ff5 lsc4">&#8710;</span></span></div><div class="t m0 x24 hb y54 ffb fs5 fc0 sc0 ls4 ws0">i</div><div class="t m0 x25 h8 y53 ff2 fs3 fc0 sc0 ls73 ws0">is<span class="_ _a"> </span><span class="ls6f">a<span class="_ _a"> </span><span class="ls56">constant<span class="_ _a"> </span><span class="ls76">in<span class="_ _7"> </span><span class="ls6b">the<span class="_ _a"> </span><span class="ls81">interv<span class="ls29">al<span class="_ _9"> </span><span class="ff5 lsbe">(<span class="ff7 lsbf">t</span></span></span></span></span></span></span></span></div><div class="t m0 x1f h9 y54 ffb fs5 fc0 sc0 ls4 ws0">i<span class="ffc lsde">&#8722;<span class="ff9 lsc5">1</span></span></div><div class="t m0 x26 hc y53 ff7 fs3 fc0 sc0 lsbc ws0">,<span class="_ _f"> </span><span class="lsbf">t</span></div><div class="t m0 x1b hb y54 ffb fs5 fc0 sc0 ls4 ws0">i</div><div class="t m0 x27 h8 y53 ff5 fs3 fc0 sc0 lsbe ws0">)<span class="ff2 ls62">.<span class="_ _a"> </span><span class="lsdf">F<span class="ls67">or<span class="_ _9"> </span><span class="ls6b">the</span></span></span></span></div><div class="t m0 xe h8 y55 ff2 fs3 fc0 sc0 ls6e ws0">ne<span class="ls76">xt<span class="_ _9"> </span><span class="ls81">interv<span class="ls29">al<span class="_ _9"> </span><span class="ff5 lsbe">(<span class="ff7 lsbf">t</span></span></span></span></span></div><div class="t m0 x28 hb y56 ffb fs5 fc0 sc0 ls4 ws0">i</div><div class="t m0 x29 hc y55 ff7 fs3 fc0 sc0 lsbc ws0">,<span class="_ _f"> </span><span class="lsbf">t</span></div><div class="t m0 x2a h9 y56 ffb fs5 fc0 sc0 ls4 ws0">i<span class="ff9 ls3d">+1</span></div><div class="t m0 x2b h8 y55 ff5 fs3 fc0 sc0 lsbe ws0">)<span class="ff2 ls62">,<span class="_ _9"> </span><span class="lse0">it<span class="_ _a"> </span><span class="ls7c">assumes<span class="_ _a"> </span><span class="ls6f">a<span class="_ _a"> </span><span class="ls9e">dif<span class="ls94">ferent<span class="_ _9"> </span><span class="ls68">v<span class="lsa6">alue.<span class="_ _9"> </span><span class="ls7a">The</span></span></span></span></span></span></span></span></span></div><div class="t m0 xe h8 y57 ff2 fs3 fc0 sc0 lsaa ws0">time<span class="_ _12"> </span><span class="ls81">interv<span class="ls9e">als<span class="_ _12"> </span><span class="ff5 lsbe">(<span class="ff7 lsbf">t</span></span></span></span></div><div class="t m0 x16 hb y58 ffb fs5 fc0 sc0 ls4 ws0">i</div><div class="t m0 x2c h8 y57 ff8 fs3 fc0 sc0 lsc0 ws0">&#8722;<span class="_ _5"> </span><span class="ff7 lsbf">t</span></div><div class="t m0 x2d h9 y58 ffb fs5 fc0 sc0 ls4 ws0">i<span class="ffc lsde">&#8722;<span class="ff9 lsc5">1</span></span></div><div class="t m0 x2e h8 y57 ff5 fs3 fc0 sc0 lsbe ws0">)<span class="ff7 lsbc">,<span class="_ _17"> </span><span class="ff8 lse1">&#8704;</span><span class="lsd7">i<span class="_ _13"> </span></span></span><span class="lsc0">=<span class="_ _12"> </span><span class="ls68">1<span class="_ _5"> </span><span class="ff7 lsbc">.<span class="_ _5"> </span>.<span class="_ _1c"> </span>.<span class="_ _5"> </span><span class="lsd8">N<span class="_ _1d"> </span><span class="ff2 ls62">.<span class="_ _12"> </span><span class="ls4d">are<span class="_ _b"> </span><span class="ls6e">assumed<span class="_ _b"> </span><span class="ls76">to<span class="_ _12"> </span></span>be</span></span></span></span></span></span></span></div><div class="t m0 xe h8 y59 ff2 fs3 fc0 sc0 ls67 ws0">of<span class="_ _8"> </span><span class="lsc">unequal<span class="_ _9"> </span><span class="lse2">widths<span class="_ _8"> </span></span></span>of<span class="_ _9"> </span><span class="ls15">size<span class="_ _9"> </span><span class="ff5 lsc4">&#8710;<span class="ff7 lsbf">t</span></span></span></div><div class="t m0 x2f hb y5a ffb fs5 fc0 sc0 ls4 ws0">i</div><div class="t m0 x30 h7 y59 ff2 fs3 fc0 sc0 ls62 ws0">.<span class="_ _8"> </span><span class="lsa8">W<span class="_ _4"></span><span class="ls6f">e<span class="_ _8"> </span><span class="ls55">assume<span class="_ _9"> </span><span class="ls2d">that<span class="_ _9"> </span><span class="ls13">this<span class="_ _8"> </span><span class="ls80">delay</span></span></span></span></span></span></div><div class="t m0 xe h7 y5b ff2 fs3 fc0 sc0 ls99 ws0">pro&#64257;le<span class="_ _c"> </span><span class="ls73">is<span class="_ _c"> </span><span class="lsa0">kno<span class="_ _1"></span><span class="ls83">wn<span class="_ _c"> </span><span class="lse3">(see<span class="_ _c"> </span><span class="lse4">Fig.<span class="_ _c"> </span><span class="lse5">(1)).</span></span></span></span></span></span></div><div class="t m0 x31 h7 y5c ff2 fs3 fc0 sc0 ls61 ws0">I<span class="_ _d"></span>I<span class="_ _d"></span>I<span class="_ _d"></span><span class="ls62">.<span class="_ _6"> </span><span class="lse6">M<span class="_ _d"></span><span class="fs4 ls63">A<span class="_ _d"></span><span class="ls66">I<span class="_ _d"></span></span>N<span class="_ _12"> </span></span><span class="lse7">R<span class="_ _14"></span><span class="fs4 ls64">E<span class="_ _d"></span><span class="ls89">S<span class="_ _d"></span><span class="ls63">U<span class="_ _d"></span></span></span>LT</span></span></span></span></div><div class="t m0 xe h7 y5d ff2 fs3 fc0 sc0 ls8c ws0">A<span class="_ _b"> </span><span class="ls80">chain<span class="_ _c"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _c"> </span><span class="ls71">for<span class="_ _c"> </span><span class="ls6c">state<span class="_ _b"> </span><span class="lsa6">estimation<span class="_ _c"> </span><span class="ls67">of<span class="_ _c"> </span><span class="ls6d">output<span class="_ _c"> </span><span class="ls2">delayed<span class="_ _c"> </span><span class="lsb9">L<span class="_ _4"></span><span class="ls6e">TI</span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 xe h7 y5e ff2 fs3 fc0 sc0 ls1b ws0">systems<span class="_ _12"> </span><span class="lsce">(described<span class="_ _b"> </span><span class="ls75">abo<span class="ls68">v<span class="ls5f">e)<span class="_ _12"> </span><span class="ls73">is<span class="_ _b"> </span><span class="ls15">deri<span class="_ _1"></span><span class="ls68">v<span class="ls87">ed.<span class="_ _12"> </span><span class="ls7a">The<span class="_ _b"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _12"> </span><span class="ls92">structure</span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 xe h7 y5f ff2 fs3 fc0 sc0 ls73 ws0">is<span class="_ _c"> </span><span class="ls96">moti<span class="_ _1"></span><span class="ls68">v<span class="ls67">ated<span class="_ _b"> </span></span>by<span class="_ _c"> </span><span class="ls6f">a<span class="_ _c"> </span><span class="lsd9">construction<span class="_ _c"> </span><span class="ls35">similar<span class="_ _c"> </span><span class="ls76">to<span class="_ _c"> </span><span class="ls6b">the<span class="_ _b"> </span><span class="ls75">one<span class="_ _c"> </span></span></span>in<span class="_ _c"> </span><span class="ls9d">[5].<span class="_ _c"> </span><span class="lsa8">W<span class="_ _4"></span><span class="ls6f">e</span></span></span></span></span></span></span></span></span></div><div class="t m0 xe h7 y60 ff2 fs3 fc0 sc0 lsc ws0">propose<span class="_ _13"> </span><span class="ls6f">a<span class="_ _16"> </span><span class="ls3b">cascade<span class="_ _13"> </span><span class="ls92">structure<span class="_ _13"> </span><span class="ls76">in<span class="_ _1"></span><span class="ls68">v<span class="ls6d">olving<span class="_ _16"> </span></span>two<span class="_ _13"> </span><span class="ls70">dynamical<span class="_ _16"> </span><span class="ls1b">systems</span></span></span></span></span></span></span></div><div class="t m0 xe h7 y61 ff2 fs3 fc0 sc0 ls71 ws0">for<span class="_ _12"> </span><span class="ls6b">the<span class="_ _b"> </span><span class="ls72">observ<span class="ls5f">er<span class="_ _12"> </span><span class="ls44">dynamics<span class="_ _12"> </span></span></span></span></span>for<span class="_ _b"> </span><span class="lsa6">estimating<span class="_ _12"> </span><span class="ls6b">the<span class="_ _b"> </span><span class="ls7c">states<span class="_ _12"> </span><span class="lse8">using<span class="_ _b"> </span></span></span>the</span></span></div><div class="t m0 xe h7 y62 ff2 fs3 fc0 sc0 ls2 ws0">delayed<span class="_ _c"> </span><span class="ls6d">output<span class="_ _c"> </span><span class="ls9">measurements.</span></span></div><div class="t m0 x32 h8 y63 ff5 fs3 fc0 sc0 lsbc ws0">&#729;</div><div class="t m0 x33 h8 y64 ff5 fs3 fc0 sc0 ls68 ws0">&#710;</div><div class="t m0 x34 ha y65 ff6 fs3 fc0 sc0 lsbd ws0">x</div><div class="t m0 x35 h9 y66 ff9 fs5 fc0 sc0 lsc5 ws0">0</div><div class="t m0 x36 h8 y65 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span>)<span class="_ _15"> </span><span class="lsc0">=<span class="_ _15"> </span><span class="ff6 lscc">A</span></span></div><div class="t m0 x7 h8 y64 ff5 fs3 fc0 sc0 ls68 ws0">&#710;</div><div class="t m0 x7 ha y65 ff6 fs3 fc0 sc0 lsbd ws0">x</div><div class="t m0 x37 h9 y66 ff9 fs5 fc0 sc0 lsc5 ws0">0</div><div class="t m0 x38 h8 y65 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span>)<span class="_ _16"> </span><span class="lsc0">+<span class="_ _16"> </span><span class="ff6 lsc2">B<span class="_ _d"></span><span class="ff7 lsc3">u</span></span></span></div><div class="t m0 x39 h9 y66 ff9 fs5 fc0 sc0 lsc5 ws0">0</div><div class="t m0 x21 h8 y65 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span>)<span class="_ _16"> </span><span class="lsc0">+<span class="_ _16"> </span><span class="ff6 lsd5">K<span class="_ _d"></span></span></span>(<span class="_ _14"></span><span class="ls68">&#175;<span class="_ _18"></span><span class="ff7 lsc6">y<span class="_ _d"></span><span class="ff5 lsbe">(</span><span class="lsbf">t<span class="ff5 lsbe">)<span class="_ _16"> </span><span class="ff8 lsc0">&#8722;<span class="_ _16"> </span><span class="ff6 lsc7">C</span></span></span></span></span></span></div><div class="t m0 x3a h8 y64 ff5 fs3 fc0 sc0 ls68 ws0">&#710;</div><div class="t m0 x3b ha y65 ff6 fs3 fc0 sc0 lsbd ws0">x</div><div class="t m0 x3c h9 y66 ff9 fs5 fc0 sc0 lsc5 ws0">0</div><div class="t m0 x1b h8 y65 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span><span class="lsc8">))<span class="_ _1e"> </span><span class="ff2 ls71">(2)</span></span></div><div class="t m0 x32 h8 y67 ff5 fs3 fc0 sc0 lsbc ws0">&#729;</div><div class="t m0 x33 h8 y68 ff5 fs3 fc0 sc0 ls68 ws0">&#710;</div><div class="t m0 x34 ha y69 ff6 fs3 fc0 sc0 lsbd ws0">x</div><div class="t m0 x35 h9 y6a ff9 fs5 fc0 sc0 lsc5 ws0">1</div><div class="t m0 x36 h8 y69 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span>)<span class="_ _15"> </span><span class="lsc0">=<span class="_ _15"> </span><span class="ff6 lscc">A</span></span></div><div class="t m0 x7 h8 y68 ff5 fs3 fc0 sc0 ls68 ws0">&#710;</div><div class="t m0 x7 ha y69 ff6 fs3 fc0 sc0 lsbd ws0">x</div><div class="t m0 x37 h9 y6a ff9 fs5 fc0 sc0 lsc5 ws0">1</div><div class="t m0 x38 h8 y69 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span>)<span class="_ _16"> </span><span class="lsc0">+<span class="_ _16"> </span><span class="ff6 lsc2">B<span class="_ _d"></span><span class="ff7 lsc3">u</span></span></span></div><div class="t m0 x39 h9 y6a ff9 fs5 fc0 sc0 lsc5 ws0">1</div><div class="t m0 x21 h8 y69 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span>)<span class="_ _16"> </span><span class="lsc0">+<span class="_ _16"> </span><span class="ff7 ls1e">e</span></span></div><div class="t m0 x3d h9 y6b ffd fs5 fc0 sc0 ls99 ws0">A<span class="ff9 lse9">&#8710;(<span class="ffb lsea">t</span><span class="lseb">)</span></span></div><div class="t m0 x3e h8 y69 ff6 fs3 fc0 sc0 lsd5 ws0">K<span class="_ _d"></span><span class="ff5 lsbe">(<span class="_ _14"></span><span class="ls68">&#175;<span class="_ _18"></span><span class="ff7 lsc6">y<span class="_ _d"></span><span class="ff5 lsbe">(</span><span class="lsbf">t<span class="ff5 lsbe">)<span class="_ _16"> </span><span class="ff8 lsc0">&#8722;<span class="_ _16"> </span><span class="ff6 lsc7">C</span></span></span></span></span></span></span></div><div class="t m0 x3f h8 y68 ff5 fs3 fc0 sc0 ls68 ws0">&#710;</div><div class="t m0 x40 ha y69 ff6 fs3 fc0 sc0 lsbd ws0">x</div><div class="t m0 x15 h9 y6a ff9 fs5 fc0 sc0 lsc5 ws0">1</div><div class="t m0 x41 h8 y69 ff5 fs3 fc0 sc0 lsbe ws0">(<span class="ff7 lsbf">t</span><span class="lsc8">))</span></div><div class="t m0 x42 h7 y6c ff2 fs3 fc0 sc0 ls71 ws0">(3)</div><div class="t m0 x1 hd y6d ffe fs6 fc0 sc0 lsd3 ws0">2008 <span class="_ _1"></span>American Control Conference</div><div class="t m0 x1 hd y6e ffe fs6 fc0 sc0 lsd3 ws0">Westin Seattle Hotel, Seattle, W<span class="_ _4"></span>ashington, USA</div><div class="t m0 x1 hd y6f ffe fs6 fc0 sc0 lsd3 ws0">June 1<span class="_ _4"></span>1-13, 2008</div><div class="t m0 x13 he y70 ffe fs7 fc0 sc0 lsd3 ws0">ThB18.1</div><div class="t m0 x1 he y71 ffe fs7 fc0 sc0 lsd3 ws0">978-1-4244-2079-7/08/$25.00 &#169;2008 <span class="_ _1"></span>AACC.<span class="_ _1f"> </span>3029</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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