Stabilizing periodic orbits of a class of mechanical systems with impulse effects: A Lyapunov constraint approach

Abstract

This paper study the stabilization of mechanical system with impulse effects around a hybrid limit cycle, the proposed control approach is based on LaSalle’s invariance principle for hybrid systems and Layounov constraint based method. Theorem 2 shows necessary and sufficient condition of the existence and the uniqueness of the developed controller which leads to a system of partial differential equations (PDE) whose solutions are the kinetic and potential energy of smooth Lyapunov function, furthermore Theorem 3 gave an alternative existence condition which states that the largest positively invariant set should be nowhere dense and closed and it is none other than the hybrid limit cycle itself.