Geometric structure of generalized controlled Hamiltonian systems and its application

The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the omega-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, called N-group, and its Lie algebra, called N-algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc, are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.