Stabilization of nonlinear switched systems using control Lyapunov functions

Abstract

In this paper, we study the stabilization of general nonlinear switched systems by using control Lyapunov functions. The concept of control Lyapunov function for nonlinear control systems is generalized to switched control systems. The first part of our contribution deals with a necessary and sufficient condition of stabilization. The main idea is to use a common control Lyapunov function, this is achieved with the converse Lyapunov theorem dedicated to switched systems. In a second part, an explicit construction of a common control Lyapunov function is addressed to a finite family of switched systems. The approach uses a family of control Lyapunov functions attached to the subsystems.

Converging algorithm for a class of BMI applied on state-dependent stabilization of switched systems

“…This has been treated in [10,11] for nonlinear switched systems via common Lyapunov functions, and in [12] for controlled nonlinear switched systems.…”

Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control

“…Switched systems have been applied in various areas, such as engine control systems, neural networks, ecosystems, mechanical systems, and even biological systems. Stability results have been derived by many researchers, via the methods of Lyapunov exponents, switched Lyapunov functions, and common Lyapunov functions (see [19][20][21][22][23]). Until now, there are few works about the switched HIV models.…”

Algebraic switching time identification for a class of linear hybrid systems

“…In the recent years, there has been an increasing interest in the control problems of switched systems due to their significance from both a theoretical and a practical point of view. Important results for switched systems have been achieved for problems including stability [3][4][5][6][7], stabilization [8][9][10][11], tracking [12] or controllability [13,14].…”