Region stability analysis for switched nonlinear systems with multiple equilibria

This paper investigates the region stability analysis 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, two methods are established, based on which several new results are then obtained for the region stability. 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 approaches to determine the corresponding regions of convergence. Moreover, an improved average dwell time (ADT) method is proposed for the stability of switched nonlinear systems whose subsystems do not share a common Lyapunov function. Finally, an illustrative example with numerical simulation is studied by using the obtained results. The study of example shows that our results work very well in analyzing the region stability of some multi-equilibrium switched nonlinear systems.

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