Safety stabilization of switched systems with unstable subsystems

This paper is concerned with the problem of safety stabilization for switched systems where the solvability of the problem under study for individual subsystems is not assumed. A new state-dependent switching strategy with guaranteed dwell-time for switched systems is constructed, and a sufficient condition for absence of Zeno behavior is derived. Also, a novel switched control design method is proposed to simultaneously guarantee the safety of the switched closed-loop system and stabilize the system based on the union of a common barrier function and a single Lyapunov function, which effectively handles the conflict between safety and stability objectives. Finally, two examples are presented to demonstrate the effectiveness of the proposed design approach.