Global Practical Stabilization of Discrete-time Switched Affine Systems via Switched Lyapunov Functions and State-dependent Switching Functions

Abstract

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via switched Lyapunov functions with the objectives of achieving less conservative stability conditions and less conservative size of the ultimate invariant set of attraction. The main contribution is to propose a state-dependent switching controller synthesis that guarantees simultaneously the invariance and global attractive properties of a convergence set around a desired equilibrium point. This set is constructed by the intersection of a family of ellipsoids associated with each of switched quadratic Lyapunov functions. The global practical stability conditions are proposed as a set of Bilinear Matrix Inequalities (BMIs) for which an optimization problem is established to minimize the size of the ultimate invariant set of attraction. A DC-DC buck converter is considered to illustrate the effectiveness of the proposed stabilization and controller synthesis method.