Improvements on PDC Controller Design for Takagi-Sugeno Fuzzy Systems with State Time-Varying Delays

Fayçal Bourahala, Kevin Guelton, F. Khaber et Noureddine Manamanni

This paper deals with the controller design for a class of T-S fuzzy model with state time varying delays. By choosing a convenient augmented Lyapunov-Krasovskii functional and employing a Parallel Distributed Compensation (PDC) control law including both memoryless and delayed state feedback, new delay dependent sufficient conditions for the stabilization of T–S fuzzy model with time-varying delay are derived in terms of linear matrix inequalities (LMIs). By taking into account the bounds of the time varying delays and its maximal rate of variation, the proposed LMI-based conditions guarantee the closed-loop asymptotic stability of the considered class of delayed T-S fuzzy systems. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design methodology and the conservatism improvement regarding to previous results.

Mots clés

Takagi-Sugeno fuzzy model, Time varying delays, Lyapunov-Krasovskii functional, Delay-dependent conditions, Linear matrix inequalities