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Stabilization of Hamiltonian systems with dissipation

Stabilization of generalized Hamiltonian systems with dissipation is investigated. First, we generalize the Casimir submanifold approach with constant controls to the static state feedback control case. Secondly, a direct Hamiltonian function method is proposed and it is shown that this method is equivalent to the Casimir sub-manifold approach. Furthermore, a dynamic state feedback control is proposed. Some sufficient conditions and a constructive process for determining controllers are provided. It is shown that the dynamic state feedback control is more powerful than the static one. Finally, the problem of a dissipative type realization of the general controlled Hamiltonian system is discussed.