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On Hamiltonian realization of time-varying nonlinear systems

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Abstract

This paper investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacobian matrix of a TVN system is nonsingular, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a non-singular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Wang YuZhen

  2. Department of Electrical and Computer Engineering, the National University of Singapore, Singapore, 117576, Singapore

    Ge S. S.

  3. Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Cheng DaiZhan

Authors
  1. Wang YuZhen
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  2. Ge S. S.
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  3. Cheng DaiZhan
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Correspondence to Wang YuZhen.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60474001), the Research Fund of the Doctoral Program of Chinese Higher Education (Grant No. 20040422059), and the Natural Science Foundation of Shandong Province (Grant No. Y2006G10)

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Wang, Y., Ge, S.S. & Cheng, D. On Hamiltonian realization of time-varying nonlinear systems. SCI CHINA SER F 50, 671–685 (2007). https://doi.org/10.1007/s11432-007-0041-6

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  • DOI: https://doi.org/10.1007/s11432-007-0041-6

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