STABILIZABILITY OF A CLASS OF NONLINEAR SYSTEMS USING HYBRID CONTROLLERS

Abstract. This paper develops hybrid control strategies for stabilizing a class of nonlinear systems. Common Lyapunov functions and switched Lyapunov functions are used to establish easily verifiable criteria for the stabilizability of weakly nonlinear systems under switched and impulsive control. Three types of controller switching rules are studied: time-dependent (synchronous), state-dependent (asynchronous) and average dwell-time satisfying. Conditions are developed for stabilizability under arbitrary switching, as well as less strict con-ditions for prespecified switching rules. Examples are given, with simulations, to illustrate the theorems developed. 1