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Stabilizability of a class of nonlinear systems using hybrid controllers. (English) Zbl 1202.93065

Summary: 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 conditions for prespecified switching rules. Examples are given, with simulations, to illustrate the theorems developed.

MSC:

93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
37C75 Stability theory for smooth dynamical systems
93D15 Stabilization of systems by feedback
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