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Stability analysis for neutral Markovian jump

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Availableonlineatwww.sciencedirect.comJournaloftheFranklinInstitute349(2012)2193–2214ShortcommunicationStabilityanalysisforneutralMarkovianjumpsystemswithpartiallyunknowntransitionprobabilities$LianglinXionga,n,JunkangTianb,XinzhiLiucaSchoolofMathematicsandComputerScience,YunnanUniversityofNationalities,Kunming650031,PRChinabSchoolofMathematicalSciences,UniversityofElectronicScienceandTechnologyofChina,Chengdu611731,PRChinacDepartmentofAppliedMathematics,UniversityofWaterloo,Waterloo,Ontario,CanadaN2L3G1Received12August2011;receivedinrevisedform18November2011;accepted5April2012Availableonline12April2012AbstractThispaperaddressestheproblemofthedelay-dependentstabilityforneutralMarkovianjumpsystemswithpartialinformationontransitionprobability.Thetimedelaysdiscussedinthispaperaretime-varyingdelays.CombinedthenewconstructedLyapunovfunctionalwiththeintroducedfreematrices,andusingtheanalysistechniqueofmatrixinequalities,thedelay-dependentstabilityconditionsareobtained.TheobtainedresultsareformulatedintermsofLMIs,whichcanbeeasilycheckedinpracticebyMatlabLMIcontroltoolbox.Threenumericalexamplesaregiventoshowthevalidityandpotentialofthedevelopedcriteria.&2012TheFranklinInstitute.PublishedbyElsevierLtd.Allrightsreserved.1.IntroductionAswellknown,neutralsystemsarefrequentlyencounteredinvariousengineeringsystems,includingpopulation,ecology,distributednetworkscontaininglosslesstransmissionlines,heatexchangers,andrepetitivecontrol.Forthelasttwodecades,agreatdealofattentionhasbeenwww.e

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