Further improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by delay-partitioning approach

Abstract

This paper focuses on further improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by a delay-partitioning approach. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then some tighter bounding inequalities, i.e., Peng-Park׳s integral inequality (reciprocally convex approach) and the Free-Matrix-Based integral inequality (which yields less conservative stability criteria than the use of Wirtinger-based inequality does) are introduced to reduce the enlargement in bounding the derivative of LKF as much as possible, therefore, less conservative results can be expected in terms of es and LMIs. Finally, a numerical example is included to show that the proposed methods are less conservative than existing ones.

Keywords: Delay-partitioning approach; Free-Matrix-Based integral inequality; Interval time-varying delay; Linear matrix inequalities (LMIs); T–S fuzzy systems.