现代控制理论教案（英文版）3

ssaryandsufficientconditionofsystem’pletelyin[to,tf]istheGramnonsingular3.PracticalyidentifyingwayA(t),B(t)’smemberis(n-2),(n-1)continuosdifferentiabletot,takeB1(t)=B(t)Ifcertaintimetf>0,thereisrankQc(tf)=n,pletelyin[0,tf].Note:sufficientcondition2.Observabilityidentification1.discussionaboutobservability1.[t0,tf]istheobservationtimeneededidentifyinginitialstate.Theinterzonerelativetoinitialtimet0.2.nonobsevableexpression3.nonsingulardonotinflactobservability2.identifyingFortimevariantsystemThenecessaryandsufficentconditionistheGram3.PracticalyidentifyingwayA(t),C(t)’smemberis(n-2),(n-1)continuosdifferentiabletot,takeC1(t)=C(t)Ifcertaintimetf>0,thereisrankRm(tf)=n,pletelyin[0,tf].3.6Thedualitybetweencontrolability&observability1.DualityrelationoflinearsystemTwosystem∑1∑22.ObservablematrixN