A generic impulsive controller for hamiltonian linear time-periodic systems

Abstract

This work introduces an impulsive controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-periodic Hamiltonian one about a periodic orbit. The controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is periodically sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into saddle, centre, or saddle-focus sub-manifolds. The novel treatment of the center manifold minimizes the system energy on it ensuring damping of oscillatory motions, which is proved crucial for controllability.