TS模糊模型的非线性时滞系统.ppt

基于T-S模糊模型的非线性时滞系统的稳定性分析及综合-Stabilityanalysisandsynthesisofnonlineartime-delaysystemsvialinearTakagiSugenofuzzymodels,主要内容,背景目的主要方法主要结论仿真验证本文亮点改进之处,一、背景,非线性时滞系统普遍存在经典方法：局部线性化方法TS模糊模型,二、主要方法,1、文主要用TS模糊模型的方法表示非线性时滞系统2、用Lyapunov函数的方法分析其稳定性3、LMI的数学技巧4、并行分布式补偿的思想,三、主要结论,无控制输入情况下的稳定的充分性条件设计状态反馈控制器，并推导了稳定的充分条件基于状态观测器的状态反馈控制器设计，并推导稳定的充分条件,定理一,用TS模型表示非线性系统：,Theorem1,Theequilibriumofthecontinuous-timefuzzysystemwithtime-delaydescribedby(6)isasymptoticallystableinthelargeifthereexistacommonmatrixP0andrmatricesSi0suchthatfori=1,2,r.,Theorem1,Proof：,Boydetal.1994,Boydetal.19942xTyxTQx+yTQ-1y其中Q0,Theorem1,Theorem1,Theorem1,Theorem1,Remark:,Theorem2,Theorem2,Theorem2,Thereexistsastatefeedbackfuzzycontrollaw(13)suchthattheequilibriumoftheclosed-loopfuzzysystemwithtime-delaydescribedby(14)isasymptoticallystableinthelargeifthereexistmatricesX0,Si0andYisatisfyingSiXandthefollowingLMIsforalliandjexceptingthepairs(i,j)suchthathi(z(t)hj(z(t)=0,t,Andthenthestatefeedbackgaincanbeconstructedas,Theorem3,Assumethatthenumberofrulesthatfireforalltislessthanorequaltoswhere10,Z,SiandYisatisfyingSiXandthefollowingLMIs:foralliandjexceptingthepairs(i,j)suchthathi(z(t)hj(z(t)=0,t,Theorem3,Proof:,Theorem3,Lemma2.Ifthenumberofrulesthatfireforalltislessthanorequaltoswhere10,X20;S1i0andS2i0;YiandRisatisfyingandtheLMIsin(36)(39)foralliandjexceptingthepairs(i,j)suchthathi(z(t)hj(z(t)=0,t.Andthenthestatefeedbackgainandobservercanbeconstructedasrespectively;fori=1,2,r.,Theorem5,Assumethatthenumberofrulesthatfireforalltislessthanorequaltoswhere10,X20;Z1-X1,Z2-X2;S1i0andS2i0;YiandRisatisfyingtheLMIsin(40)and,Theorem5,foralliandjexceptingthepairs(i,j)suchthathi(z(t)hj(z(t)=0,t.Andthenthestatefeedbackgainandobservercanbeconstructedasrespectivelyfori=1,2,r.,四、仿真实验,continuous-timetruck-trailermodel：,四