Robust fuzzy stabilization of nonlinear time-delay systems subject to impulsive perturbations

Abstract This paper is concerned with robust stabilization problem of Takagi–Sugeno (T-S) fuzzy time-delay systems subject to impulsive perturbations. New results on robust stabilization via parallel distributed compensation (PDC) control are derived. First, based on the impulse-type Razumikhin–Lyapunov method combined with the use of an impulse-time-dependent Lyapunov function, a new exponential stability criterion for T-S fuzzy time-delay system with impulsive effects is obtained. The proposed stability criterion removes the restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results. Then, by employing a convex relaxation technique, a sufficient condition for the constructing the PDC controllers is presented, which is expressed in terms of linear matrix inequalities (LMIs). Next, the robust stabilization problem for the T-S system with slowly time-varying delay is studied. A different stabilization condition is derived via an impulse-time-dependent Lyapunov functional, which is less conservative than the former when the state delay is constant. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed analysis and design techniques.