robust admissible analyse of uncertain singular systems via delta operator method

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1、RobustAdmissibleAnalyseofUncertainSingularSystemsviaDeltaOperatorMethod　　【Abstract】Thispaperinvestigatestheproblemofrobustadmissibleanalysisforuncertainsingulardeltaoperatorsystems（SDOSs）.Firstly,weintroducethedefinitionofgeneralizedquadraticadmissib

2、ilitytoensurerobustadmissibility.Then,bymeansofLMI,anecessaryandsufficientconditionisgiventoproveauncertainSDOSisgeneralizedquadraticadmissible.Finally,anumericalexampleisprovidedtodemonstratetheeffectivenessoftheresultsinthispaper.　　【Keywords】SDOSs;

3、Ｒobustadmissibility;LMI　　0　Introduction　　Singularsystemwasproposedinthe1970s[1].Ithasirreplaceableadvantagesovernormalsystem[2].Whennormalsystemmodeldescribespracticalsystem,itrequiressystemiscircular.Thereisoutputderivativeexistingininversesystem,an

4、ditcausesnormalsystemisnotcircular.Singularsystemsdonothavethisdrawback.Anycontrolsystemshaveuncertainfactor[3].Adeltaoperatormethodwaspresentedinthe1980sbyGoodwinandMiddleton[4].Afterthat,wehaveobtainedalotoftheoretical9achievements.Wecanobtaindelta

5、operatorasfollows:　　1　Preliminaries　　Thesenotationsareputtouseinthispaper:Rnmeansn-dimensionalrealvectorsetsandRm×nmeansm×ndimensionalrealmatrixsets.TheidentitymatrixwithdimensionrisdenotedbyIr.MatrixQ＞0（orQ＜0）meansthatQispositiveandsymmetricdefinite

6、（ornegativedefinite）.?姿（E，A）={?姿∈Cdet（?姿E-A）=0}.TherankofamatrixAisdenotedbyrank（A）.Dint（b，r）istheinterioroftheregionwiththecenterat（b，0）andtheradiusequaltoIinthecomplexplane.Theshorthanddiag（S1，S2...Sq）meansthematrixisdiagonalmatrixwithmaindiagonalm

7、atrixbeingthematricesS1，S2...Sq.　　ConsideringthebelowSDOSdescribedby：　　E?啄x（tk）=A?啄x（tk）（１）　　wheretkmeansthetimet＝kh.Thesamplingperiodhsatisfyh＞0.x（tk）∈Rnisthestate.E,A?啄∈Rn×nareknownconstantmatrices,and0＜rank（E）=r＜n.　　Definition1[5]：If?姿（E,A?啄）?奂Din

8、t（-1/h，1/h）,wecallthesystem（１）isstable.Ifdeg（det（?啄E-A?啄））=rank（E）,wecallthesystem（１）iscausal.Ifdet（?啄E-A?啄）isnotidenticallyzero,wecallthesystem（１）isregular.Ifitisregular,causalandstab1e,wecallthesystem（１）iscausal.9　　Consideringthebelowsingulardiscre