隶属度函数相关的T-S模糊时滞系统稳定性准则  

A Membership-dependent Stability Criterion for T-S Fuzzy Systems with Time Varying Delay

作　　者：郭娜娜 姜偕富[1] 尹宗明[1] 唐亮 GUO Nana;JIANG Xiefu;YIN Zongming;TANG Liang(School of Automation,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学自动化学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2020年第4期63-69,共7页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61673148)。

摘　　要：研究一类T-S模糊时滞系统的稳定性问题。首先,充分利用时滞信息构造一个新的隶属度函数相关的增广型L-K泛函;其次,基于李雅普诺夫稳定性定理,采用Jensen积分不等式、Wirtinger积分不等式和凸组合相结合的方法来处理L-K泛函求导过程中产生的积分项,与隶属度函数相关的项则通过建立切换规则来处理;然后,以矩阵不等式的形式给出一个保守性较小的稳定性准则;最后,通过一个通用数例来验证准则的有效性。The stability of Takagi-Sugeno(T-S) fuzzy systems with time-varying delay is studied in this paper. Firstly, on the basis of augmented Lyapunov-Krasovskii(L-K) functional approach, a new membership function dependent L-K functional is constructed by employing more information of time delay. Then, based on Lyapunov stability theory, Jensen integral inequality, Wirtinger integral inequality and convex combination are employed to estimate the integral terms of derivative of the L-K functional, and switching rules are established to avoid the time derivative of membership functions. Next, improved stability criterion is proposed in the form of Linear Matrix Inequalities(LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed criterion in this paper.

关 键 词：L-K泛函 T-S模糊模型 时变时滞 稳定性准则 隶属度函数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]