Switched Systems Stabilization by Means of Time-Dependent Switching Signal

Abstract

The stabilization problem of the switched system is investigated by employing both stabilizing and destabilizing switching instants under the time-dependent switching signal. A new piece-wise Lyapunov function is proposed to distinguish the switching instants, which utilizes dwell time information. For tolerance of unstable modes, globally exponentially stable conditions are derived, which compensates for state divergence that resulted from unstable modes and destabilizing switching instants by stabilizing switching instants. The method is extended to the controller design of the switched linear system and inspires a necessary and sufficient condition for the switched linear systems with pairwise commutative. Finally, simulation is applied to verify the effectiveness of the methods.