Abstract: The problems of stability analysis and control design for nonlinear time-delay systems represented by a (Takagi-Sugeno, T-S) fuzzy model are investigated. Firstly, a novel integral inequality is chosen to dispose the integral term in the derivative of the Lyapunov-Krasovskii functional, and then the less conservative delay-dependent stability conditions are obtained. Secondly, combining with Finsler lemma, a fuzzy state feedback controller design strategy by means of linear matrix inequalities (LMIs) is presented under the parallel distributed compensation (PDC) technique. Finally, two numerical examples are given to show the effectiveness of the presented stability analysis and control strategy.

Key words: Takagi-Sugeno (T-S) fuzzy model, time-delay systems, integral inequality, parallel distributed compensation (PDC) technique

摘要： 研究了(Takagi-Sugeno, T-S)模糊模型描述的非线性时滞系统的稳定性分析和控制器设计问题。首先，选取一个新的积分不等式用以处理求导Lyapunov-Krasovskii泛函所得的积分项，进而提出了保守性较小的时滞依赖稳定性条件。其次，结合Finsler引理，以线性矩阵不等式(LMIs)形式给出了基于并行分布补偿(PDC)技术的模糊状态反馈控制器设计策略。最后，给出2个仿真实例用以证明给出的稳定性分析和控制策略的有效性。

关键词: Takagi-Sugeno (T-S)模糊模型, 时滞系统, 积分不等式, 并行分布补偿(PDC)