Abstract:

Finite time stability and stabilization are studied for hybrid dynamic systems. By combining multiple Lyapunov function and finite time Lyapunov function, a sufficient condition of finite time stability is given for the system. Compared with the previous works, our results have less conservativeness. Furthermore, based on the state partition of continuous and resetting parts of system, a hybrid feedback controller is constructed, which stabilizes
the closed-loop systems in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Key words: hybrid dynamic systems, multiple Lyapunov function, finite time Lyapunov function, stability, stabilization