几类奇异摄动系统的鲁棒控制研究

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1、ABSTRACThaveextensiveapplicationsintheareaofSingularperturbationsystemsandtechnology，andtherobustcontrolofwhichhasbeenstudiedengineeringrecentlybymanyresearcherswhoarefromdifferentfields．Amongallkindsisanone．ofmethodsproposedsingularperturbationtechniqueimpor

2、tantHowever，uptothepresent，itisessentialconditionthatthecoefficientmatrixisofstatevariableinthesystemisnonsingularwhentheoriginalsystemdecomposedintotwosubsystems：aslowreducedsystemandafastrestricttheuseofthesingularperturbationboundary．1ayersystem，whichthis，

3、inthisdissertation，attentionisfocusedonthetheory．Consideringantosolverobustcontroldevelopmentofsingularperturbationapproachforsingularlyperturbedsystemswithpulsebehavior．Themainproblemsresultsobtainedinthisdissertationareasfollows：Firstly，westudytheglobalrobu

4、ststabilizationproblemforaclassofisnonlinearuncertainsingularperturbationsystems．Whentherepulseforbehaviorinperturbationsystems，thecompostedrobustfeed-backcontrolthewholesystemswasobtainedbyapplyingthetwo·timescaledesigntheoremandinequalityskill，andtheupperst

5、abilityapproach，matrixanalysisisboundofsmallparameter￡wasalsogiven．Finally，anumericalexampleprovidedtodemonstratetheeffectivenessandfeasibilityofthedesignmethod．withtime_delayandpulseSecondly，asingularlyperturbedsystemforstabilityisbehaviorisconsidered．Corres

6、pondingsufficientconditionobtainedintermsofthetwo-timescaledesignapproach，Lyapunovstabilityiterativedesignprocedurefortheoryandlinearmatrixinequality(LMI)．Anthestabilizingcontrollerisalsopresented．Numericalexamplesaregiventoillustratetheefficacyoftheproposeda

7、pproach．forthenonlinearthree—speciesFinally，thesingularlyperturbedproblemsfood．．chainreactiondiffusionsystemsareconsidered．Byusingthedifferentialmeanvaluetheoremandthemethodofupperandlowersolutions，thebehaviorofthesolutionfortheinitialboundaryvalueproblemsiSa

8、symptoticstudied．Moreover，theexistenceanduniquenessofsolutionfortheoriginallIproblemandtheuniformlyvalidasymptoticestimationarealsodiscussed．Keywords：singularlyperturbedsystems；uncertaint