隶属函数依赖的时变时滞模糊系统的控制

Membership-function-dependent control of fuzzy systems with time-varying delays

摘要:

研究了时变时滞TS模糊系统的稳定性分析和镇定问题.首先,构造一个增广LyapunovKrasovskii函数,结合自由权矩阵不等式,以线性矩阵不等式(LMIs)形式给出了时滞依赖的稳定性准则.基于状态空间分割技术,构造一些由子空间的局部上下确界的凸组合表示的分段隶属函数去近似逼近隶属函数,充分考虑隶属函数的边界信息,同时引入松弛矩阵,进而得到了更为放松的隶属函数依赖的稳定性结果;其次,基于前提不匹配技术,提出了变时滞模糊系统的状态反馈控制器的设计方法,其隶属函数及模糊规则数目可以自由选取,从而提高了控制器设计的灵活性;最后,给出三个仿真实例证明所提方法的有效性.

Abstract:

This paper investigates the stability analysis and stabilization for T-S fuzzy systems with time-varying delays. Firstly, an augmented Lyapunov-Krasovskii functional is constructed, delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining with the free-matrix-based integral inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions, which can be locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions, the boundary information of the membership functions is taken into consideration adequately, meanwhile, some slack matrices are employed, and then some relaxed membership-function-dependent stability results are obtained. Secondly, state feedback controllers for the fuzzy systems with time-varying delays are presented under the imperfect premise matching technique, whose membership functions and the number of fuzzy rules are allowed to be designed freely, consequently, the flexibility of controller design is improved. Finally, two numerical examples are given to demonstrate the effectiveness of the presented approaches.