TS模糊模型的非线性时滞系统

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-delaysystemsvialinearTakagi–Sugenofuzzymodels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：Theorem1Theequilibriumofthecontinuous-timefuzzysystemwithtime-delaydescribedby(6)isasymptoticallystableinthelargeifthereexistacommonmatrixP0andrmatricesSi0suchthatfori=1,2,…r.Theorem1Proof：Boydetal.1994Boydetal.19942xTy≤xTQx+yTQ-1y其中Q0Theorem1Theorem1Theorem1Theorem1Remark:Theorem2Theorem2Theorem2Thereexistsastatefeedbackfuzzycontrollaw(13)suchthattheequilibriumoftheclosed-loopfuzzysystemwithtime-delaydescribedby(14)isasymptoticallystableinthelargeifthereexistmatricesX0,Si0andYisatisfyingSi≥XandthefollowingLMIsforalliandjexceptingthepairs(i,j)suchthathi(z(t))hj(z(t))=0,∨t,AndthenthestatefeedbackgaincanbeconstructedasTheorem3Assumethatthenumberofrulesthatfireforalltislessthanorequaltoswhere1s≤r.Thereexistsastatefeedbackfuzzycontrollaw(13)suchthattheequilibriumoftheclosed-loopfuzzysystemwithtime-delaydescribedby(14)isasymptoticallystableinthelargeifthereexistmatricesX0,Z,SiandYisatisfyingSi≥XandthefollowingLMIs:foralliandjexceptingthepairs(i,j)suchthathi(z(t))hj(z(t))=0,∨tTheorem3Proof:Theorem3Lemma2.Ifthenumberofrulesthatfireforalltislessthanorequaltoswhere1s≤r,thenTheorem3Theorem4Theorem4Theorem4Theorem4Theorem4Theorem4Theorem4Theequilibriumoftheclosed-loopfuzzytime-delaysystemwithobserver-basedcontrollaw(25)describedby(28)isasymptoticallystableinthelargeifthereexistmatricesX10,X20;S1i0andS2i0;YiandRisatisfyingandtheLMIsin(36)–(39)foralliandjexceptingthepairs(i,j)suchthathi(z(t))hj(z(t))=0,∨t.Andthenthestatefeedbackgainandobservercanbeconstructedasrespectively;fori=1,2,…r.Theorem5Assumethatthenumberofrulesthatfireforalltislessthanorequaltoswhere1s≤r.Theequilibriumoftheclosed-loopfuzzytime-delaysystemwithobserver-basedcontrollaw(25)describedby(28)isasymptoticallystableinthelargeifthereexistmatricesX10,X20;Z1≥-X1,Z2≥-X2;S1i0andS2i0;YiandRisatisfyingtheLMIsin(40)andTheorem5foralliandjexceptingthepairs(i,j)suchthathi(z(t))hj(z(t))=0,∨t.Andthenthestatefeedbackgainandobservercanbeconstructedasrespectivelyfori=1,2,…r.四、仿真实验continuous-timetruck-trailermodel：四、仿真实验四、仿真实验五、本文亮点工作量大T-S模糊模型数学技巧六、改进之处李雅普诺夫函数的构造可以改进。LMI求公共的P具有保守性，如果r比较大，公共的P未必存在。谢谢！！