Convergence domain for time-varying switched systems

In this paper, we investigate the convergence domain for time-varying switched systems. We construct multiple Lyapunov functions and each Lyapunov function is decreasing outside a ball whose radius is time-varying. We give a relatively accurate convergence domain for a general time-varying switched system. Finally, a numerical example, a mass–spring–damper system, is provided to show the effectiveness of the theoretical results.