Stability analysis of nonlinear reset control systems with smooth baseline modes

In this paper, we are concerned with stability of nonlinear reset control systems whose baseline modes are smooth enough. It is well-known that the existence of a strict Lyapunov function of the baseline system and the dissipativeness of the reset mapping imply asymptotical stability of a reset system. The main purpose of this paper is to show that, if only a weak Lyapunov function is available to prove the stability of the baseline system, then the asymptotical stability can be still assured provided that the reset mapping is dissipative and the baseline dynamics is smooth enough.