Attractors and limit cycles of discrete-time switching affine systems: Nominal and uncertain cases

Abstract

This paper deals with the robust stabilization of uncertain discrete-time switched affine systems using a control Lyapunov approach and a min-switching state-feedback control law. After presenting some preliminaries on limit cycles, a constructive stabilization theorem, expressed as linear matrix inequalities, guarantees that the solutions to the nominal closed-loop system converge to a limit cycle. This method is extended to the case of uncertain systems, for which the notion of limit cycle needs to be adapted. The theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature.