Abstract
In this paper, a stabilizing controller is designed for a finite or infinite set of nonlinear time-varying systems with unknown parameters under certain hypotheses on the set of the plants, namely, compactness and Lyapunov controllability assumptions. A switching control law is utilized for the purpose of stabilization, which, different from general variable structure control (VSC) strategy, possesses a finite number of switches before asymptotic stability of the systems is achieved. Lyapunov direct method will be used for designing both the control law and the switching index. The main result of this paper could be considered as the extension of adaptive stabilization method for linear systems proposed by Fu and Barmish (1986) to adaptive control for nonlinear system.
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