Stability and stabilization of T–S fuzzy systems with time delay via Wirtinger-based double integral inequality

Abstract

Abstract This paper concerns the issue of stabilization and stability analysis for Takagi–Sugeno (T–S) fuzzy systems with time delay. A new type of Lyapunov–Krasovskii functional (LKF), including Non-Quadratic Lyapunov functional and triple integral term, is introduced to obtain stability conditions of fuzzy time-delay systems. A Wirtinger-based double integral inequality is used to estimate integral term, and the free weighting variable technique is also employed for controller syntheses and stability analysis. Additionally, less conservative and newer stability conditions with delay-dependent are proposed in the form of linear matrix inequalities (LMIs). Furthermore, Several examples are provided to illustrate how effective the suggested approaches are.