Robust dynamic output‐feedback ℋ∞ control for uncertain Takagi–Sugeno time‐delay systems

Abstract

This work deals with the problem of robust output‐feedback control for a class of uncertain Takagi–Sugeno (T‐S) fuzzy systems with state time‐varying delays. The system is described by a state‐space T‐S fuzzy model with time‐varying delays and norm‐bounded parameter uncertainties. A robust control strategy via Lyapunov–Krasovskii functionals for stability and performance conditions is derived. The T‐S fuzzy‐model‐based framework is employed in analysis, and formulations are performed based on the solution of a set of delay‐dependent linear matrix inequalities (LMIs). By solving the derived LMI conditions via a convex programming toolbox, a full‐order robust dynamic output‐feedback controller is designed. The obtained robust output‐feedback controller guarantees asymptotic stability of the closed‐loop system and provides an norm, that is, disturbance attenuation level, for all admissible uncertainties. In this sequel, three examples are given to reveal the effectiveness and merits of the proposed approaches.

On Separation Principle in Dynamic Output Controller Design for One Class of Takagi-Sugeno Fuzzy Systems

“…which implies (14). As a consequence, the inequality (42) has to be satisfied, which introduces an additive matrix inequality…”

“…It is natural to use ODC for systems with a T-S fuzzy model using an ODC in the parallel distributed form [13], [14], where these advanced approaches are compared in simulations. The results demonstrate the applicability of the robust control design using a non-fragile form of ODC and the descriptor approach in terms of LMIs in [15].…”