时滞切换正系统的切换齐次协正Lyapunov函数方法-论文.pdf

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1、第40卷第4期西南民族大学学报·自然科学版JournalofSouthwestUniversityforNationalities．NaturalScienceEditionJul2014doi：10．3969／j．issn．1003-4271．2014．04．24【特约专稿】SwitchedhomogeneouscopositiveLyapunovfunctionmethodforswitchedpositivesystemswithdelaysLIUXing—wen(SchoolofElectricalandInformationEngineeri

2、ng，SouthwestUniversityforNationalities，Chengdu610041，ER．C．)Abstract：Positivesystemsareaspecialclassofsystemswhosestatesalwayslieinthepositiveorthantprovidedthattheinitialconditionsarenonnegativeandswitchedsystemsareoneofmainbranchesofhybridsystems．Asacombinationofpositivesystems

3、andswitchedsystems，switchedpositivesystemshavegainedrapidlyincreasingattentionmthecommunityofcontro1．Thispaperaddressesthestabilityproblemofswitchedpositivesystemswithdelays．ThemethodofswitchedhomogeneouscopositiveLyapunovfunctionisproposedtoreduceconservativenessofstabilitycrit

4、erionoftheconsideredsystem．Manyexistingresultsaredegeneratedcasesofourmainconclusion．Keywords：delays；switchedpositivesystem；switchedhomogeneouscopositiveLyapunovfunction；stability中图分类号：TP27文献标识码：A文章编号：1003—4271(2014)04．0592．061IntroductionItiswidelyknownthatmanyphysicalsystemsin

5、therealworldinvolvevariablesthathavenonnegativesign．say,populationofanimalsandabsolutetemperature．SuchsystemsarereferredtoaspositivesystemsLlJ．Roughlyspeaking，positivesystemsmeanthattheirstatesandoutputsarenonncgativewhenevertheinitialconditionsandinputsarenonnegative，andhavenum

6、erousapplicationsinareassuchaseconomics，biology,andsociology．⋯Recentl~theimportanceofswitchedlinearpositivesystems(SLPSs)hasbeenhighlightedbymanyresearcherst2-sJ．Itshouldbenotedthat，eventhoughthemainpropertiesofbOthpositivesystemsandgeneralswitchedlinearsystemsarewellunderstood，

7、manybasicquestionsrelatedtoSLPSsremainunanswered。AsfarasSLPSisconcerned，stabilityandstabilizationareitsmostimportantdynamics．Thispaperwil1explorethestabilityissueofsuchclassofsystems．Whenstabilityofpositivesystemsisconsidered．itisnaturaltoadopt1inearcopositiveLyapunovfunction．Th

8、isapproachcapturesthenatureofpositivity,andhasb