Practical exponential set stabilization for switched nonlinear systems with multiple subsystem equilibria

Abstract

This paper studies the practical exponential set stabilization problem for switched nonlinear systems via a t -persistent approach. In these kinds of switched systems, every autonomous subsystem has one unique equilibrium point and these subsystems’ equilibria are different each other. Based on previous stability results of switched systems and a set of Gronwall–Bellman inequalities, we prove that the switched nonlinear system will reach the neighborhood of the corresponding subsystem equilibrium at every switching time. In addition, we constructively design a suitable t -persistent switching law to practically exponentially set stabilize the switched system. Finally, a numerical example is presented to illustrate the obtained results.