Singular Perturbation Analysis of Energy Control Systems

In this paper the known conditions for the stability of singularly perturbed speed-gradient based control systems are extended to encompass the problems of speed-gradient based energy control of singularly perturbed Hamiltonian systems. General stability results for singularly perturbed nonlinear systems are given, which apply to the energy control of Hamiltonian systems. The application to controlled synchronization of two coupled pendulums is presented for two cases of the appearance of a small parameter in the system: the small inertia of a dynamical coupling link and the small inertia of a torquer. In both cases, comparison between asymptotic theoretical accuracy bounds and computer simulation results is performed.