Improved stability criteria for T-S fuzzy systems with time-varying delay by delay-partitioning approach

• DOI: 10.1007/s12555-014-0394-8
• Publication Date: 2015-09-26T14:15:39Z
• Authors: Jun Yang; Wen-Pin Luo; Yong-Hu Wang; Chun-Sheng Duan
• Keywords: Bounding overwatch; Lemma (botany); Linear matrix inequality

This paper focuses on the robust stability criteria of uncertain T-S fuzzy systems with timevarying 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.