Region stability analysis for switched nonlinear systems with multiple equilibria

This paper investigates the region stability for switched nonlinear systems whose subsystems have different equilibria, which are referred to multi-equilibrium switched nonlinear systems, and proposes a number of new results on the region stability analysis. Through investigating the dynamical behavior of the multi-equilibrium switched system, a Common Lyapunov-like (CL-like) function method and a Multiple Lyapunov-like (ML-like) function method are established for the region stability, based on which several new approaches to the region stability analysis are then obtained. It is shown that the main results obtained in this paper not only guarantee the region stability of the multi-equilibrium switched nonlinear system under arbitrary switching, but also provide several new methods to determine the corresponding stable regions. Finally, several illustrative examples with numerical simulations are studied by using the results obtained in this paper. Study of examples shows that our analysis methods work very well in analyzing the region stability of some classes of multi-equilibrium switched linear systems.