expontial+stabihty+of+stochastic+systems+with+hysteresis+switching

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3、8cJe,ƱúÙØ©Ü©½ÜSN.£Ø©3)Åd5½¤Ø©ö¶µ¶µFϵcFÁ©ïÄ´ÅXÚê½5.EÅXÚ),3ùp==Ä¢,Ù5K6uG,G5K±w´«4O.duüfXÚm1,ÅXÚØU÷vÛÜLipschitz^.3{',·ÑÌ(J´:NA^DynkinúªÚêت,òÝê½5Úa.s.ê½5âí2ÅXÚ.ÏLO^,/ÏBurkholder-Davis-Gundyت,?ØÝê½5Úa.s.ê½5m'X.©

4、ÏLÑý~f,=:üؽfXÚm,ÅXÚ´ê½,lyâk5.'cÅXÚ,XÚ,¢,G,ê½.iAbstractForstochasticswitchedsystems,theexponentialstabilityisconsideredinthispa-per.Toconstructthesolutionoftheswitchedsystem,weonlyfocusonthehysteresisswitchingrulewhichisstate-dependentandc

5、anbeviewedasaclosed-loopcontrolscheme.Comparedwiththeexistingmethods,themaindifficultycomesfromhowtoapplyDynkin’sformulaandexponentialmartingaleinequalitytothecasewherelocallyLipschitzconditionsaredestroyedbyswitchingbehaviors.Thecriteriaonmomentexpone

6、ntialstabilityandalmostsureexponentialstabilityofthestochasticswitchedsystemareestablished.Therelationsbetweenmomentexponentialstabilityandalmostsureexponentialstabilityforstochasticswitchedsystemsarediscussedrequiringaddi-tionalconditionsbytheaidoft

7、heBurkholder-Davis-Gundyinequality.Thesimulationexamplesthatunstablesubsystemscanbeswitchedtoanexponentiallystableswitchedsystemisgiventoillustratethevalidityoftheresults.KeywordsStochasticsystems,Switchedsystem,Hysteresisswitching,State-dependentswi

8、tch-ing,Exponentialstability.ii8¹Á...................................................................iAbstract...............................................................ii1Introduction.........................................................11.1B

9、ackground.................................................11.2Mainwork.................................................21.3Generalnotation.............................................22Deterministicswitchedsystems.....................................