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一类离散Markov跳跃系统基于状态观测器的鲁棒H_∞控制.docx

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一类离散Markov跳跃系统基于状态观测器的鲁棒H_∞控制 Introduction Markovjumpsystemsaredynamicsystemsthatcanchangetheirbehaviorrandomlyorwithcertainprobabilities.Thesesystemsarewidelyusedinvariousfieldssuchascontrol,communicationsystems,andfinance.However,uncertaintyanddisturbancesoftenexistinpracticalapplications,whichmakethedesignofrobustcontrolmethodsforsuchsystemsachallengingtask.ThispaperdiscussestheproblemofrobustH_∞controlforaclassofdiscrete-timeMarkovjumpsystemswithstateobservers. ProblemStatement Consideraclassofdiscrete-timeMarkovjumpsystemsdescribedbythefollowingequation: x(k+1)=Ax(k)+Bw(k)+Δ(k) y(k)=Cx(k)+v(k) wherex(k)isthestatevector,y(k)istheoutputvector,w(k)isthesysteminput,Δ(k)istheunknowndisturbancewithaboundednorm,andv(k)isthemeasurementnoisewithzeromeanandboundednorm.Aisaconstantsystemmatrixwithappropriatedimensions,andBandCareconstantinputandoutputmatrices,respectively. Thesystemissubjecttomodechanges,whichoccuraccordingtoaMarkovchainwithstatespaceS={1,2,...,m},transitionprobabilitymatrixP=[p_ij],andinitialprobabilitydistributionπ=[π_i].Whenthesystemisinmodeiattimek,thetransitionprobabilityofmodechangetomodejattimek+1isp_ij.Themodesequenceisdescribedbytherandomvariableσ(k),whichtakesvaluesinS. ThegoalistodesignarobustH_∞controllerthatensurestheclosed-loopsystemisstableandachievesaspecifiedH_∞performancelevel.Thecontrollerconsistsofastateobserverandastatefeedbackcontroller,andshouldbeabletoguaranteerobustperformanceagainstdisturbancesandmeasurementnoise. RobustH_∞ControlDesign TodesignarobustH_∞controllerfortheMarkovjumpsystem,thefollowingstepsaretaken: 1.MarkovJumpLinearSystemModeling Thesystemdynamicscanbedescribedas: x(k+1)=Aσ(k)x(k)+Bw(k)+Δ(k) y(k)=Cx(k)+v(k) wherethesystemmatrixAσ(k)dependsonthecurrentmodeσ(k).ThisisaMarkovjumplinearsystem(MJLS),whichcanberepresentedasacollectionoflineartime-invariant(LTI)systemsindexedbytheMarkovchainstate.Theideaistodesignamode-dependentobservertoestimatethesystemstateandmodesequence. 2.Mode-DependentObserverDesign Themode-depend