State switching of a multistable impacting system using PD-like control

A new PD-like control law is proposed in this paper to control a multistable impacting system. This control law can switch the system from a current, undesired state to a desired one by using the differences of the displacement and velocity between the current and desired states. The control law can control the multistable system without affecting its original dynamics, and its stability is proved by using the Lyapunov direct method. Numerical results are compared with the results obtained by using the intermittent control studied in [1]. The proposed PD-like control shows a better performance in terms of the smoothness of its control signal, which is easier to be implemented in practical applications.