Stability of switched systems with multiple equilibria: a mixed stable-unstable subsystem case

This paper studies the stability of switched systems that are composed of a mixture of stable and unstable modes with multiple equilibria. The main results of this paper include some sufficient conditions concerning set convergence of switched nonlinear systems. We show that under suitable dwell-time and leave-time switching laws, trajectories converge to an initial set and then stay in a convergent set. Based on these conditions, Linear Matrix Inequality (LMI) conditions are derived that allow for numerical validation of the practical stability of switched affine systems, which include those with all unstable modes. Two examples are provided to verify the theoretical results.