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Geometric structure of generalized controlled Hamiltonian systems and its application

  • Daizhan Cheng
  • Zairong Xi
  • Qiang Lu
  • Shengwei Mei
Article

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.

Keywords

generalized Hamiltonian system symplectic geometry symplectic group Poisson bracket excitation control 

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Copyright information

© Science in China Press 2000

Authors and Affiliations

  • Daizhan Cheng
    • 1
  • Zairong Xi
    • 1
  • Qiang Lu
    • 2
  • Shengwei Mei
    • 2
  1. 1.Laboratory of Systems and Control, Institute of Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Department of Electrical EngineeringTsinghua UniversityBeijingChina

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