Abstract
The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the ω-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, calledN-group, and its Lie algebra, calledN-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.
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Cheng, D., Xi, Z., Lu, Q. et al. Geometric structure of generalized controlled Hamiltonian systems and its application. Sci. China Ser. E-Technol. Sci. 43, 365–379 (2000). https://doi.org/10.1007/BF02916984
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DOI: https://doi.org/10.1007/BF02916984