Stabilising slow-switching laws for switched discrete-time linear systems

For a class of switched discrete-time linear systems, a state-dependent switching law with dwell time is designed to make the overall system asymptotically stable. A main feature is that the Lyapunov-like function may not be monotonically decreasing in both time-driven and state-driven periods, and this feature allows the proposed stabilising switching law being of lower switching frequency in contrast with recent results. An illustrative example is employed to show the effectiveness of the proposed switching law. Furthermore, it is shown that the proposed switching law ensures that a bounded perturbation implies bounded states, and a convergent perturbation implies convergent states. When the system state is not available, an observer-based state-dependent switching law with dwell time is also developed.