A Lyapunov functional approach to impulsive control of Takagi-Sugeno fuzzy delay systems

This paper considers impulsive control of the Takagi-Sugeno (T-S) fuzzy delay systems with known bounds on the impulsive intervals. A piecewise differentiable Lyapunov functional is introduced to analyze exponential stability of T-S delay systems under impulsive control. The Lyapunov functional is discontinuous at the impulse times. We provide a set of LMI-based conditions that guarantee the decrease of the Lyapunov functional after the impulse times, from which stability follows. By solving linear matrix inequalities, a state feedback fuzzy impulsive controller that can stabilize the considered time-delay system can easily be obtained. Finally, an example is provided to illustrate the effectiveness of the proposed approach.