Exponential Stability and Asynchronous Stabilization of Nonlinear Impulsive Switched Systems via Switching Fuzzy Lyapunov Function Approach

In this paper, the Takagi–Sugeno (T-S) fuzzy model is first used to deal with the exponential stability and asynchronous stabilization problem of a class of continuous-time nonlinear impulsive switched systems with asynchronous behaviors. In order to reduce the conservativeness resulting from the quadratic Lyapunov functions (QLFs) and nonlinearity, the switching fuzzy Lyapunov functions (FLFs) are proposed using the switching information and structural information of membership function in the rule base. Using the switching FLFs approach and the mode-dependent average dwell time (MDADT) technique, we obtain stability conditions for the open-loop nonlinear impulsive switched systems and stabilization conditions for the closed-loop nonlinear impulsive switched systems. Moreover, the stability and stabilization results are formulated in the form of LMIs. Finally, a numerical example and a chemical process example are given to demonstrate the advantage and applicability of the proposed method.