Robust stability and stabilization for fuzzy systems with neutral and distributed delays

Abstract

In this paper, we consider the stability and stabilization of Takagi-Sugeno fuzzy systems with neutral and distributed delays. We employ a generalized Lyapunov functional to obtain delay-dependent stability conditions of such a fuzzy time-delay system. We introduce some free matrices to such a Lyapunov functional in order to reduce the conservatism in stability conditions. These techniques lead to generalized and less conservative conditions. Applying the same techniques made on the stability conditions, we obtain delay-dependent conditions for the robust stability of uncertain fuzzy systems with neutral and distributed delays. Moreover, we consider the robust stabilization. Based on the robust stability conditions on the closed-loop system, we give design methods of the state feedback controllers for uncertain fuzzy time-delay systems. Finally, we give two examples to illustrate our results.