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一类随机时滞系统的鲁棒控制.docx

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一类随机时滞系统的鲁棒控制 Title:RobustControlforaClassofRandomTime-DelaySystems Abstract: Inthispaper,weinvestigatetheproblemofrobustcontrolforaclassofrandomtime-delaysystems.Time-delaysystemsareencounteredinvariousengineeringfields,andthepresenceofrandomdelayscanintroduceuncertaintiesthatmaydegradesystemperformanceorevencauseinstability.Thus,developingrobustcontrolstrategiestohandletheseuncertaintiesbecomescrucial.Inthisstudy,weproposearobustcontrolapproachthatcaneffectivelyaddressthechallengesposedbyrandomtimedelays.Theproposedcontrolstrategyisdesignedtoaccountforuncertaintiesinsystemdynamicsandtimedelays,ensuringstableandsatisfactorysystemperformance.Simulationresultsdemonstratetheeffectivenessandefficiencyoftheproposedrobustcontrolscheme. 1.Introduction Time-delaysystemsfindwideapplicationsinvariousfields,suchastelecommunications,chemicalprocesses,andtransportationsystems.Thepresenceoftimedelaysinthesesystemscanleadtopoorperformanceoreveninstability.Randomtimedelays,whichareencounteredinmanypracticalscenarios,couldfurtherexacerbatetheseissues.Thus,developingrobustcontrolmethodstohandletheuncertaintiescausedbyrandomtimedelaysisofgreatimportance. 2.SystemModeling Inthissection,wepresentthemathematicalmodelfortheclassofrandomtime-delaysystemsconsideredinthisstudy.Thesystemdynamicsaredescribedbyasetofstochasticdifferentialequations,incorporatingbothdeterministicandstochasticterms.Therandomtimedelaysareassumedtofollowacertainprobabilitydistribution.Wealsodiscusstheimpactsoftheserandomtimedelaysonsystemstabilityandperformance. 3.RobustControlDesign Toaddressthechallengesposedbyrandomtimedelays,weproposearobustcontrolstrategybasedonH∞controltechniques.Thecontroldesignaimstominimizetheeffectofuncertaintiesanddisturbancesbyintroducingpropercontrollawsthataccountforthesystemdynamicsandtimedelays.Therobustcontrolapproachguaranteesstabilityandimprovesperformanceunderrandomtimedelays. 4.StabilityAnalysis Weconductathoroughstabilityanalysisoftheproposedrobustcontrolscheme.ByutilizingLyap