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1、第40卷第4期西南民族大學(xué)學(xué)報(bào)·自然科學(xué)版JournalofSouthwestUniversityforNationalities．NaturalScienceEditionJul2014doi：10．3969／j．issn．1003-4271．2014．04．24【特約專(zhuān)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中圖分類(lèi)號(hào)：TP27文獻(xiàn)標(biāo)識(shí)碼：A文章編號(hào)：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
