Robust observer-driven switching stabilization of switched linear systems

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1、JControlTheoryAppl201311(1)69–73DOI10.1007/s11768-013-2011-4Robustobserver-drivenswitchingstabilizationofswitchedlinearsystemsJunWU†,ZhendongSUNCollegeofAutomationScienceandEngineering,SouthChinaUniversityofTechnology,GuangzhouGuangdong510640,ChinaAbstract:Inthiswork,wes

2、tudytherobustobserver-drivenswitchingstabilizationproblemofswitchedlinearsys-tems.Undertheconditionthateachsubsystemiscompletelyobservable,withtheobserver-drivenswitchinglawwhichmakesthesystemexponentiallystableforthenominalsystem,weprovethattheoverallsystemisrobustagain

3、ststruc-tural/switchingperturbationsandisinput/outputtostatestableforunstructuralperturbations.Keywords:Switchedlinearsystems;Observer-drivenswitchingstabilization;Robustness1IntroductionrobustanalysisofthesystemisintroducedinSection3.Sec-Aswitchedlinearsystemisahybridsy

4、stemwhichcon-tion4presentsanillustrativeexample.Finally,Section5sistsofafinitenumberoflinearsubsystemsandaswitchingconcludesthework.lawgoverningtheactivenessofthosesubsystems.Sincethe1990s,switchedlinearsystemshavebeenattractingmuch2Preliminariesandpreparationsattention,n

5、otonlyfortheirtheoreticalchallengesbutalsoLetRbethesetofrealnumbers,·betheEuclideanforthepracticalimportance;see,forinstance,[1–3].FornormforavectorinRnandtheinducednormforamatrixswitchedlinearsystems,themainresearchtopicsaretheinRn×n.dynamicbehavioranalysis,suchasstab

6、ility[4–5],observ-Consideraswitchedlinearsystemdescribedbyability[6–7],andstabilizingswitchingdesign[8–10].x˙(t)=Aσ(t)x(t),(1)Inpractice,perturbationsmayenterintoanysystem.Generally,theperturbationsforaswitchedsystemcanbey(t)=Cσ(t)x(t),(2)wherex(t)∈Rnisthestate,y(t)∈Rpis

7、themeasuredout-imposedonthesubsystemdynamics,theswitchingmech-anism,orboth.Thus,therobustswitchingdesignproblem,put,σ(t)∈M={1,2,...,m}istheswitchingsignal/lawtobedesigned,andA∈Rn×n,C∈Rp×n,i∈Marewhichistofindproperswitchingmechanismsthatmaketheiisystemstableandattenuatepos

8、sibleperturbations,isnatu-realconstantmatrices.Letφ(t;t0,x0,σ)denotethemotionrallyraisedandhasreceivedm