Abstract
The switched system with possible unstable modes 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 property of the switching instants with the help of dwell time information. Then, globally exponentially stable conditions of the switched nonlinear system and the switched linear system are derived, respectively, which compensate the state divergence resulted from unstable modes and destabilizing switching instants by stabilizing switching instants. The related result is extended to the controller design of the switched linear system. Besides, for the switched linear systems with pairwise commutative, a necessary and sufficient condition is proposed based on a new time-dependent switching signal, which provides a novel way for the controller design of the switched system. Finally, simulation is presented to show the effectiveness of our results.
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