前提不匹配的模糊时滞系统镇定条件的改进

Improved stabilization condition for delayed fuzzy systems under imperfect premise matching

本文研究了前提不匹配的Tagaki-Sugeno(T–S)模糊时滞系统的镇定问题.与一般的T–S模糊时滞系统相比,该系统中模糊模型与模糊控制器拥有不同的模糊规则数与不同的隶属度函数.基于Lyapunov稳定性理论,通过引进新型积分不等式,给出了包含隶属度函数信息的镇定条件.本文提出的新方法充分考虑了隶属度函数的信息,同时得到了Lyapunov函数导数的最小下界,因此新的镇定条件比以往结果具有更小的保守性.另一方面给出前提不匹配的控制器设计方法,由于模糊控制器的隶属度函数可以任意选取,因此提高了控制器设计的灵活性.最后仿真实例证明了本文方法的有效性及优越性.

This paper focuses on the stabilization issue for Tagaki-Sugeno(T–S)fuzzy systems with time-delay under imperfect premise matching.Comparing with the traditional T–S fuzzy time-delay system,the fuzzy model and fuzzy controller share different number of fuzzy rules and different premise membership functions in the systems we discussed.Based on the Lyapunov stability theory,a novel stabilization condition containing the information of membership functions is proposed on the basis of an improved integral inequality.The proposed method can make full use of the information of the membership functions.Meanwhile,the minimum lower bound of the derivative of Lyapunov function is obtained.Therefore,the new stabilization criteria is less conservative than previous results.On the other hand,a new design approach under imperfect premise matching is also developed,which enhances the design flexibility as the membership functions of the fuzzy controller can be chosen arbitrarily.Furthermore,illustrative examples are given to demonstrate the effectiveness and advantages of our approaches.