Stabilization of a class of mechanical systems with impulse effects by Lyapunov constraints

This paper presents a new theoretical control approach for the feedback stabilization of a class of mechanical systems with impulse effects that is based on using Lyapunov conditions of asymptotic stability as kinematic affine constraints [8] where the corresponding constraint force is the control force. We prove that the condition of existence and uniqueness lead to a system of partial differential equations whose solution is the required Lyapunov function, as a result we apply this approach to design a controller to stabilize limit cycles of a compass-gait biped.