Semiglobal stabilization of nonlinear uncertain systems via a lyapunov-based switching logic

Abstract

An adaptive supervisory switching control scheme for nonlinear uncertain systems is developed. Such a scheme comprises: A family of nonlinear candidate controllers, designed using a convex control design methodology

and a Lyapunovbased switching criterion that orchestrates which of the candidate controllers should be put in feedback with the uncertain plant. The family of candidate controllers is designed in such a way that, for every portion of the uncertainty set there is one Lyapunov function whose derivative is decreasing with a prescribed rate. Such Lyapunov functions are used by the switching logic to assess which is the most suitable controller to be put in feedback. The resulting scheme guarantees semiglobal stability with desired transient performance, in terms of decaying rate of the derivative of the Lyapunov function. © 2013 IEEE.