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1、JournalofMathematicalResearch&ExpositionVol.18,No.4,5232528,November1998XTheDisturbanceRejectioninSingularSystemsFanWentaoTanLiansheng(WuhanInsituteofMathematicalSciences,AcademicSinica,Wuhan430071)AbstractUsinglinearstatefeedbackandlinearfeedforwardcont
2、rolofthedisturbances,theproblemofachievingthedistrubancerejectioninalineartimeinvariantsingularsystemistreatedandaconstructivesolvabilitycondi2tionispresented.Keywordssingularsystem,disturbancerejection,invariantsubspace,feed2forwardcontrol,statefeedback
3、,subspacerecursion.ClassificationAMS(1991)93C45öCCLTP273I.IntroductionInrecentyears,therehasbeenagrowinginterestinthesystem2theoreticproblemofsin2gularsystems(orgeneralizedstate2spacesystems)duetotheextensiveapplicationsofsingu2larsystemsinlarge2scalesys
4、tems,singularperturbationtheory,circuits,economics,controltheory,andotherareas.Disturbancerejectionisafeedbacksynthesisproblemconcerningasystemwithadistur2banceasaninput.Thepurposeofdisturbancerejectionistoapplyfeedbackinsuchawaythatthedisturbancehasnoin
5、fluenceonthecontrolledoutputoftheclosed2loopsystem.Thedevelopmentofnecessaryandsufficientconditionsforthesolvabilityofthisproblemforstate2spacesystemsbyWonhametalhasprofoundinfluenceongeometrycontroltheory,particularlybymeansofan(A,B)2invariantsubspace.n
6、Inthispaper,westudydisturbancerejectionforthesingularsystems.LetX=R,U=mplR,Y=R,D=R.Weconsiderthetime2invariantsingularsystemoftheformaEx(t)=Ax(t)+Bu(t)+S1d(t),(1.1a)y(t)=Cx(t),(1.1b)whereE,A:X→X,B:U→X,C:X→Y,S1:D→XarelinearmapswithEsingular.x(t),y(t),u(t)
7、,d(t)arefunctionsoftimewithvaluesinX,Y,U,Drespectively,d(t)repre2sentsthedisturbanceasaninputtothesystem.WeinvestigatethequestionsofwhenandhowthelinearmapF:X→U,F1:D→XinthestatefeedbackandlinearfeedforwardcontrolofthedisturbancesXReceivedOctober30,1995.—5
8、23—©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.u(t)=2(Fx(t)+F1d(t))(1.2)maybechosensothattheoutputy(t)oftheclosed2loopsystemaEx(t)=(A-BF)x(t)+Sd(t)(1.3a)y(t)=Cx(t)(1.3b)isindependentofd(t),andtheclosed2l
