时变时滞T-S模糊系统稳定性判据的改进  

Improved Stability Criterion for T-S Fuzzy Systems with Time-Varying Delay

作　　者：高倩[1] 林崇[1] 程倩倩[1] 张俊强[1] 

机构地区：[1]青岛大学复杂性科学研究所,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2015年第4期31-36,共6页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金资助项目(61174033);山东省自然科学基金资助项目(ZR2011FM006)

摘　　要：本文针对时变时滞T-S模糊系统的稳定性问题,通过构造适当的Lyapunov-Krasovskii泛函,利用Wirtinger型积分不等式和倒数凸组合相结合的方法,给出了新的判断系统时滞相关稳定性的充分条件,并用数值算例进行验证。验证结果表明,当τ(t)为时变时滞,τ(t)的上界d2取不同值时,定理1获得的最大时滞上界值均大于文献[11],[13]和[14]的结果,说明本文方法所得到的结果与Jensen不等式和时滞分割等方法相比,具有更小的保守性,且文献[11]采用了时滞分割法,证明本方法的有效性和优越性。因此,本方法为时变时滞T-S模糊系统的镇定及性能控制研究提供了理论依据。In this paper, the stability analysis for T-S fuzzy systems with time-varying delay is studied. By constructing an appropriate type of augmented Lyapunov-Krasovskii functional and using the Wirtingerbased integral inequality and the reciprocally convex method, a new method is presented in terms of linear matrix inequalities. A numerical example is given to illustrate that the upper bound of the maximum time delay obtained by the present method is higher than those of the[17]-[19]. It shows that the proposed method is less conservative compared with some other methods of Jensen inequality and delay-decomposition,and this shows the validity and superiority of this method. It can provide a theoretical basis for deal ing with stabilization and performance control for T-S fuzzy systems with time-varying delay.

关 键 词：T-S模糊系统 LYAPUNOV-KRASOVSKII泛函 Wirtinger型积分不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]