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 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 Theorem1 Theequilibriumofthecontinuous timefuzzysystemwithtime delaydescribedby 6 isasymptoticallystableinthelargeifthereexistacommonmatrixP 0andrmatricesSi 0suchthatfori 1 2 r Theorem1 Proof Boydetal 1994 Boydetal 19942xTy xTQx yTQ 1y其中Q 0 Theorem1 Theorem1 Theorem1 Theorem1 Remark Theorem2 Theorem2 Theorem2 Thereexistsastatefeedbackfuzzycontrollaw 13 suchthattheequilibriumoftheclosed loopfuzzysystemwithtime delaydescribedby 14 isasymptoticallystableinthelargeifthereexistmatricesX 0 Si 0andYisatisfyingSi XandthefollowingLMIsforalliandjexceptingthepairs i j suchthathi z t hj z t 0 t Andthenthestatefeedbackgaincanbeconstructedas Theorem3 Assumethatthenumberofrulesthatfireforalltislessthanorequaltoswhere10 Z SiandYisatisfyingSi XandthefollowingLMIs foralliandjexceptingthepairs i j suchthathi z t hj z t 0 t Theorem3 Proof Theorem3 Lemma2 Ifthenumberofrulesthatfireforalltislessthanorequaltoswhere1 s r then Theorem3 Theorem4 Theorem4 Theorem4 Theorem4 Theorem4 Theorem4 Theorem4 Theequilibriumoftheclosed loopfuzzytime delaysystemwithobserver basedcontrollaw 25 describedby 28 isasymptoticallystableinthelargeifthereexistmatricesX1 0 X2 0 S1i 0andS2i 0 YiandRisatisfyingandtheLMIsin 36 39 foralliandjexceptingthepairs i j suchthathi z t hj z t 0 t Andthenthestatefeedbackgainandobservercanbeconstructedasrespectively fori 1 2 r Theorem5 Assumethatthenumberofrulesthatfireforalltislessthanorequaltoswhere10 X2 0 Z1 X1 Z2 X2 S1i 0andS2i 0 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