A note on switching signal of switched linear systems

In this paper, we address stability analysis of switched linear systems with average dwell time switching signal. We focus on the properties of stabilizer switching signal beside the controller design. For switched systems with average dwell time switching signals, we provide a condition in terms of upper bound of the decay rate and a lower bound of the average dwell-time, in which exponentially stability is guaranteed. Based on the Lyapunov function technique, we want to merge switching signal technique, which satisfy the average dwell time, minimize a cost function, and give minimum number of subsystems to be stabilized.