Reachable set estimation and synthesis of discrete-time switched systems

This article focuses on estimating the reachable set of discrete-time switched linear systems with unknown disturbance. The discontinuous multiple Lyapunov function, which enables us to reduce the conservatism in the sense of mode-dependent average dwell-time, is proposed to estimate the underlying reachable set. The main difficulty of this problem is that the energy may jump at the switching instants. To this end, we seek for another set, which preserves the former reachable set as an inner one, guaranteeing that in the case of escaping the inner reachable set at the switching instants, the state trajectory will arrive at the inner reachable set within finite time. Finally, two numerical examples are given to show the efficiency of the proposed strategy.