Global convergence analysis for piecewise linear systems applied to limit cycles in a DC/DC converter

This paper utilizes recent results in the stability analysis of piecewise linear systems and closed orbits. A discrete-time framework with Lyapunov arguments is used. The technique has been used in the literature to prove global stability for a wide range of systems with hybrid behavior. The objectives are to obtain non-conservative LMI-formulations of the Lyapunov stability resulting in good estimation of the convergence rate for the system. It is shown how the convergence properties in discrete time is related to continuous-time convergence. The results are applied to a DC/DC voltage converter.