Observer-Based Control of Takagi–Sugeno Descriptor System with Time-Varying Delay: Free-Weighting Matrix

This article investigates the stability/stabilization problem for Takagi–Sugeno (T–S) descriptor systems with time-varying delay. A transformation-based model has been employed through a two-term approximation, and the input-output approach has been investigated using the small gain Theorem. A novel free-weighting matrix method, in combination with a new construct Lyapunov–Krasovskii functional (LKF), has been developed. Delay-dependent conditions have been obtained in a set of linear matrix inequalities (LMIs). To estimate the system states T–S fuzzy descriptor observer-based controller has been introduced. The gains have been designed using a new design strategy. Finally, three examples have been borrowed to test the merit and the validity of the proposed method. © 2022 John Wiley & Sons Ltd.