On the global practical stabilization of discrete-time switched affine systems: application to switching power converters

Abstract

This paper presents new sufficient conditions as a set of Bilinear Matrix Inequalities (BMIs) for the global practical stabilization of discrete-time switched affine systems. The main contribution is on proposing the stability conditions based on a common quadratic Lyapunov function that can be used to stabilize the discrete-time switched affine systems around a desired equilibrium point for which it is not required to find any Schur stable convex combination of operating modes as a pre-processing stage, that needs special algorithms and is an NP-hard problem. The result is that the existing two-stage stabilization methods based on a pre-calculation of a Schur stable convex combination of operating modes are simplified to a single-stage method by which a high degree of applicability is obtained. The proposed stability conditions are developed in a way the size of the convergence ellipsoid is minimized. Moreover, it is not required the equilibrium point, around which the invariant set of attraction is constructed, be inside a predetermined set of attainable equilibrium points. The satisfactory operation of the proposed stability conditions is illustrated by an academic example and application on various DC-DC converters.