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In this note, based on the control Lyapunov function approach, a new method for solving the feedback stabilization problem of switched systems that are switching arbitrarily between two multiinput nonlinear subsystems is introduced. Necessary and sufficient conditions for the existence of globally uniformly asymptotically stabilizing state feedback controllers are derived. Additionally, a universal formula for constructing implementable stabilizing controllers is given when the presented conditions hold. One numerical example is given to illustrate the results.