|Stabilizing Periodic Orbits of a Class of Mechanical Systems with Impulse Effects: A Lyapunov Constraint Approach
Mohammed Chaalal* and Noura Achour
International Journal of Control, Automation, and Systems, vol. 15, no. 5, pp.2213-2221, 2017
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."
"Compass-gait biped, control force, hybrid limit cycle, LaSalle’s invariance principle, Lyapunov constraints, mechanical systems with impulse effects, nowhere dense set, PDE."