Brief Generalized Hamiltonian realization of time-invariant nonlinear systems

Authors:
Yuzhen Wang;Chunwen Li;Daizhan Cheng
Affiliations:
Department of Automation, Tsinghua University, Beijing 100084, China and School of Control Science and Engineering, Shandong University, Jinan 250061, China;Department of Automation, Tsinghua University, Beijing 100084, China;Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

A key step in applying the Hamiltonian function method is to express the system under consideration into a generalized Hamiltonian system with dissipation, which yields the so-called generalized Hamiltonian realization (GHR). In this paper, we investigate the problem of GHR. Several new methods and the corresponding sufficient conditions are presented. A major result is that if the Jacobian matrix of a time-invariant nonlinear system is nonsingular, the system has a GHR whose structure matrix and Hamiltonian function are given in simple forms. Then the orthogonal decomposition method and a sufficient condition for the feedback dissipative realization are proposed.