Robust switching control design using Lur'e Lyapunov functions

Abstract

This article addresses the problem of robust output regulation for uncertain switched systems. A general result is first proposed for the case of uncertain and nonlinear systems. In order to cope with model uncertainties, the proposed approach implements the internal model principle. Local asymptotic stability of the closed‐loop system as well as zero steady state error on the controlled output are proven using Lur'e Lyapunov functions. Then, this result is specialized to the linear case. Sufficient conditions ensuring global or local stability of the closed loop system are provided. Furthermore, a constructive method based on LMI is presented. When only local stability is achieved, outcomes of this procedure are not only the controller gains, but also an estimation of the robust domain of attraction. Finally, illustrative examples are proposed, showing the efficiency of the proposed methods.