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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,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,-Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi,Sugeno,fuzzy models,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：,Theorem 1,The equilibrium of the continuous-time fuzzy system with time-delay described by (6) is asymptotically stable in the large if there exist a common matrix P0 and r matrices,S,i,0 such that,for i=1,2,r.,Theorem 1,Proof,：,Boyd et al. 1994,Boyd et al. 1994,2x,T,yx,T,Qx+y,T,Q,-1,y,其中,Q0,Theorem 1,Theorem 1,Theorem 1,Theorem 1,Remark:,Theorem 2,Theorem 2,Theorem 2,There exists a state feedback fuzzy control law (13) such that the equilibrium of the closed-loop fuzzy system with time-delay described by (14) is asymptotically stable in the large if there exist matrices X0,S,i,0 and Y,i,satisfying,S,i,X,and the following,LMIs,for all i and j excepting the pairs (i ,j) such that,h,i,(z(t)h,j,(z(t,)=0,t, And then the state feedback gain can be constructed as,Theorem 3,Assume that the number of rules that fire for all t is less than or equal to s where 10,Z,S,i,and Y,i,satisfying,S,i,X,and the following,LMIs,:,for all i and j excepting the pairs (,i,j,) such that,h,i,(z(t)h,j,(z(t,)=0,t,Theorem 3,Proof:,Theorem 3,Lemma 2,.,If the number of rules that fire for all t is less than or equal to s where 10,X20;S1i0 and S2i0;Yi and,Ri,satisfying,and the,LMIs,in (36)(39) for all i and j excepting the pairs (,i,j,) such that,h,i,(z(t)h,j,(z(t,)=0, t. And then the state feedback gain and observer can be constructed as,respectively; for i=1,2,r.,Theorem 5,Assume that the number of rules that fire for all t is less than or equal to s where 10,X20;Z1-X1,Z2-X2;S1i0 and S2i0;Yi and,Ri,satisfying the,LMIs,in (40) and,Theorem 5,for all i and j excepting the pairs (,i,j,) such that,h,i,(z(t)h,j,(z(t,)=0, t. And then the state feedback gain and observer can be constructed as,respectively for i=1,2,r.,四、仿真实验,continuous-time truck-trailer model,：,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！,
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