|Improved Stability Criteria for T-S fuzzy Systems with Time-varying Delay by Delay-partitioning Approach
Jun Yang*, Wen-Pin Luo, Yong-Hu Wang, and Chun-Sheng Duan
International Journal of Control, Automation, and Systems, vol. 13, no. 6, pp.1521-1529, 2015
Abstract : This paper focuses on the robust stability criteria of uncertain T-S fuzzy systems with time-varying delay by delay-partitioning approach. An appropriate Lyapunov-Krasovskii functional is established in the framework of state vector augmentation. Then, on the basis of the Finsler’s lemma, some tighter bounding inequalities (Seuret-Wirtinger’s integral inequality and Peng-Park’s integral inequality) are employed to deal with (time-varying) delay-dependent integral items. Therefore, less conservative delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs), which can be solved efficiently with the Matlab LMI toolbox. Finally, two numerical examples are provided to show that the proposed conditions are less conservative than existing ones.
Keyword : Delay-partitioning approach, Linear matrix inequalities (LMIs), Lyapunov-Krasovskii functional (LKF), Stability, Time-varying delay, Takagi-Sugeno (T-S) fuzzy systems.