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

Document Type: Article

Author

Department of Electrical Engineering, Sahand University of Technology, Sahand New Town, Tabriz, P.O. Box: 51335-1996, Iran

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.

Keywords