Exponential stability of impulsive systems with application to uncertain sampled-data systems

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1、ARTICLEINPRESSSystems&ControlLetters()–www.elsevier.com/locate/sysconleExponentialstabilityofimpulsivesystemswithapplicationtouncertainsampled-datasystemsPayamNaghshtabrizi∗,JoaoP.Hespanha,AndrewR.Teel˜DepartmentofElectricalEngineeringattheUniversityofCalifornia,SantaBarbar

2、a,UnitedStatesReceived22February2007;receivedinrevisedform6October2007;accepted8October2007AbstractWeestablishexponentialstabilityofnonlineartime-varyingimpulsivesystemsbyemployingLyapunovfunctionswithdiscontinuityattheimpulsetimes.Ourstabilityconditionshavethepropertythatw

3、henspecializedtolinearimpulsivesystems,thestabilitytestscanbeformulatedasLinearMatrixInequalities(LMIs).ThenweconsiderLTIuncertainsampled-datasystemsinwhichtherearetwosourcesofuncertainty:thevaluesoftheprocessparameterscanbeunknownwhilesatisfyingapolytopicconditionandthesam

4、plingintervalscanbeuncertainandvariable.Wemodelsuchsystemsaslinearimpulsivesystemsandweapplyourtheoremtotheanalysisandstate-feedbackstabilization.Wefindapositiveconstantwhichdeterminesanupperboundonthesamplingintervalsforwhichthestabilityoftheclosedloopisguaranteed.Thecontro

5、ldesignLMIsalsoprovidecontrollergainsthatcanbeusedtostabilizetheprocess.Wealsoconsidersampled-datasystemswithconstantsamplingintervalsandprovideresultsthatarelessconservativethantheonesobtainedforvariablesamplingintervals.c2007ElsevierB.V.Allrightsreserved.Keywords:Impulsiv

6、esystems;Uncertainsampled-datasystems;Exponentialstability;Networkedcontrolsystems1.Introductioncanfindapositiveconstantwhichdeterminesthemaximumsamplinginterval.IntheNCSsliteraturethismaximumImpulsivedynamicalsystemsexhibitcontinuousevolutionssamplingintervalisoftencalledτM

7、ATI,e.g.,in[2].WeshowtypicallydescribedbyOrdinaryDifferentialEquations(ODEs)thatourconditionsimproveuponpreviousresultsinthesenseandinstantaneousstatejumpsorimpulses.Weestablishthattheclosed-loopsystemremainsstableforlargersamplingexponentialstabilityofnonlineartime-varying

8、impulsiveintervals.Wealsoconsiderthecontroldesignproblem,insystems.Thenweconsiders