On the Asymptotic Stability of Nonlinear Time-Varying Switched Systems

Abstract

This paper considers a class of nonlinear systems with switching from one nonstationary Lienard-type equation to another. For such a system, the asymptotic stability of a given equilibrium is studied using the method of Lyapunov functions and theory of differential inequalities. The switching law constraints that guarantee the desired property of the system are established. As shown below, these constraints generally depend on the rate of change of time-varying system parameters. Some illustrative examples are also given.