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1、Systems&ControlLetters61(2012)127–133ContentslistsavailableatSciVerseScienceDirectSystems&ControlLettersjournalhomepage:www.elsevier.com/locate/sysconle✩OntheasymptoticstabilityofswitchedhomogeneoussystemsA.Yu.Aleksandrova,∗,A.A.Kosovb,A.V.PlatonovaaFaculty
2、ofAppliedMathematicsandControlProcesses,St.PetersburgStateUniversity,35UniversitetskijPr.,198504Petrodvorets,St.Petersburg,RussiabInstituteofSystemDynamicandControlTheory,SiberianBranchoftheRussianAcademyofSciences,134LermontovaStr.,664033,Irkutsk,Russiaart
3、icleinfoabstractArticlehistory:ThestabilityofswitchedsystemsgeneratedbythefamilyofautonomoussubsystemswithhomogeneousReceived15July2010right-handsidesisinvestigated.ItisassumedthatforeachsubsystemtheproperhomogeneousLyapunovReceivedinrevisedformfunctionisco
4、nstructed.ThesufficientconditionsoftheexistenceofthecommonLyapunovfunction14July2011providingglobalasymptoticstabilityofthezerosolutionforanyadmissibleswitchinglawareobtained.Accepted21October2011InthecasewherewecannotguaranteetheexistenceofacommonLyapunovf
5、unction,theclassesofAvailableonline24November2011switchingsignalsaredeterminedunderwhichthezerosolutionislocallyorgloballyasymptoticallystable.Itisprovedthat,foranygivenneighborhoodoftheorigin,onecanchooseanumberL>0(dwelltime)Keywords:suchthatifintervalsbet
6、weenconsecutiveswitchingtimesarenotsmallerthanLthenanysolutionoftheSwitchedsystemsAsymptoticstabilityconsideredsystementersthisneighborhoodinfinitetimeandremainswithinitthereafter.Lyapunovfunction©2011ElsevierB.V.Allrightsreserved.HomogeneoussystemsDwelltim
7、e1.IntroductionHowever,theproblemoftheexistenceofaCLFhasnotgotacon-structivesolutionevenforthecaseoffamilyoflinearstationaryInrecentyears,therehasbeenanincreasinginterestinthesystems[1,2,14].stabilityanalysisofswitchedsystemsduetotheirsignificanceInthesitua
8、tionswherewecannotprovetheexistenceofabothintheoryandapplications[1–3].AswitchedsystemisaCLFfortheconsideredfamily,theasymptoticstabilityofswitchedparticularkindofhybriddynamicalsystemthatconsistsofasy
