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1、具有时滞的线性区间系统鲁棒稳定性第15卷第1期1998年2月控制理论与应用CoNTROLTHEORYANDAPPLICATIONSVo1.15,No.1Feb.,1998RobustStabilityofLinearIntervalSystemswithTime—DelayNIANXiaohong(DepartmentofMathematics,TianshuiTeacher'sCollege?Gansu,741001,PRC)Abstract:Inthispaper,someresultsforrobuststabilityoflinearint
2、ervaltime—delaysystemsarederivedandsoE~epreviouscriteriaforstabilityoflineartime—delaysystemsarefurtherdevei—opedtthestabilitydegreearealsodiscussed.Finally,therobuststabilityoflarge—scalelinearinter—valtime—delaysystemisstudied.K+ywords:intervalmatrixFrobuststability;time—del
3、ayFlarge—scalesystem1IntroductionSincetime—delayisfrequentlyencounteredinvariousengineeringsystems,thestudyoftime—delaysystemshasprovidedconsiderableinterestsamongresearchersfrombothhomeandabroad.Manymethodstocheckthestabilityoftime—delaysystemswereobtainedbyMoriandKokame:,Hma
4、med[,Wangeta1.[,additionally,sincetherobuststabilityisuse—f1】1indesigningcontrolsystems.therobuststabilityofintervalsystemsisalsostudiedbymanyauthors.Manyresultstotesttherobuststabilityofuncertaintime—delaysystemswereproposedbyWangandLin,LiuY.Q.andTangG.Y.:53,ShyuandYan:.Inthi
5、spaper,wewillstudyrobustlystabilityofsystemG,..EDtE-h'Iz(f)一(),∈,O].…'.2RobustStabilityofLinearIntervalTime—DelaySystemConsiderthelineartime—delaysystemdescribedbythefollowingintervaldifferential—dif—ferenceequations:cix∈(外二G,EDx(ttEhO3¨'I)一0),∈一,.Wherez∈受isastatevector,matric
6、esGEB,C3,G[D,E]areXintervalmatrices,h>0isaconstant,￡)isacontinuousvector—valuedinitialfunction,A一(口)…,B一()rC一(ciJ)…rD一(d0),E一(F,)…arematrices.LetA.一寺(B+c),K一寺(c—B),M(m)…,m一max{lI,I￡,1);,—l,2,…,;foranyA∈GEB,C3,A】∈G[D,E],considersystem主(f)一Aox(t)+(A—Ao)z(￡)+A】x(t一^).(2.2)Thes
7、ystem(2.1)issaidtoberobustlystableifforanyA∈GEB,c],Al∈G[D,E],system(2.2)isasymptoticstable.Definition2.1Thesystem(2.1)issaidtohavestabilitydegree>0,ifthereexistsk>0(dependingoninitialconditions),suchthatanysolutionof(2.2)satisfiesedbreye2n2ceF9oundeavtiseiondJaofn.gGan.1
8、9suProv"舶"?'No.1RobustStabilityofLinearIntervalSystemswithtim
