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1、ANZIAMJ.49(2007),111129DELAY-DEPENDENTSTABILITYANDSTABILIZATIONOFUNCERTAINDISCRETE-TIMEMARKOVIANJUMPSINGULARSYSTEMSWITHTIMEDELAYSHUPINGMA12,XINZHILIU34andCHENGHUIZHANG3(Received9December,2006;revised5June,2007)AbstractThispaperdiscussesrobuststochasticstabili
2、tyandstabilizationoftime-delaydiscreteMarkovianjumpsingularsystemswithparameteruncertainties.Basedontherestrictedsystemequivalent(RES)transformation,adelay-dependentlinearmatrixinequalitiescon-ditionfortime-delaydiscrete-timeMarkovianjumpsingularsystemstobere
3、gular,causalandstochasticallystableisestablished.Withthiscondition,problemsofrobuststochasticstabilityandstabilizationaresolved,anddelay-dependentlinearmatrixinequalitiesareobtained.Anumericalexampleisalsogiventoillustratetheeffectivenessofthismethod.2000Math
4、ematicssubjectclassi?cation:primary39A12;secondary93C55.Keywordsandphrases:discreteMarkovianjumpsingularsystem,time-delaysystem,delay-dependent,linearmatrixinequality(LMI),robuststochasticstabilityandstabilization.1.IntroductionInpractice,manydynamicalsystems
5、cannotberepresentedbylineartime-invariantmodelssincethedynamicsofsomefeaturesofthesesystems,suchasforexample,abruptchanges,breakdownsofcomponents,changesintheinterconnectionsofsub-systems,etc.,arerandom.Suchclassesofdynamicalsystemsfallintothecategoryofstocha
6、stichybridsystems.AspecialclassofhybridsystemsreferredtoasMarkovianjumpsystems,whichexhibitrandomstructures,hasattractedmuchinterestamongresearchersandmanyimportantproblemsinvolvingthesesystemshavebeeninves-tigated,suchasstability,stabilizationandH∞controlpro
7、blems,see[4,5,6,8,18]1SchoolofMathematicsandSystemScience,ShandongUniversity,Jinan,250100,China;e-mail:mashup@sdu.edu.cn.2SchoolofComputerScienceandTechnology,ShandongUniversity,Jinan,China.3SchoolofControlandEngineering,ShandongUniversity,Jinan,250061,China.
8、4DepartmentofAppliedMathematics,UniversityofWaterloo,Waterloo,Ontario,CanadaN2L3G1;e-mail:xzliu@uwaterloo.ca.cAustralianMathematicalSociety2007,Serial-feecode1446-8735/07111112ShupingMa,
