Stabilization of aperiodic sampled-data switched affine systems to hybrid limit cycles

Abstract

This paper deals with the stabilization of aperiodic sampled-data switched affine systems to a predetermined hybrid limit cycle using a hybrid dynamical system representation and a control Lyapunov function approach. Some preliminaries on the hybrid dynamical system formalism provide the framework for modeling switched affine systems followed by definitions on hybrid limit cycles and related notions. The main result, based on simple Linear Matrix Inequalities (LMI), guarantees that the solutions to the closed-loop system converge to a hybrid limit cycle defined by the states, functioning modes with their corresponding dwell times. The theoretical results are evaluated on academic examples and demonstrate the potential and the originality of the method over the recent literature.