Communications in Information and Systems

Volume 2 (2002)

Number 2

Pseudo-Hamiltonian realization and its application

Pages: 91 – 120



Daizhan Cheng (Institute of Systems Science, Chinese Academy of Sciences, Beijing, China)

Tielong Shen (Department of Mechanical Engineering, Sophia University, Tokyo, Japan)

T. J. Tarn (Department of Systems Science and Mathematics, Washington University, St. Louis, Missouri, U.S.A.)


In this paper, the problem of pseudo-Hamiltonian realization of a control system is studied. Several sufficient conditions are obtained. The stability of a dynamic system is investigated via dissipative pseudo-Hamiltonian realization, and the stabilization of a control system is also investigated via feedback dissipative pseudo-Hamiltonian realization. Some relations between the stability (asymptotical stability) with the dissipative (strict dissipative) realization are revealed. Relations between the affine dissipative control systems and the dissipative pseudo-Hamiltonian realization are also investigated. These results show that the set of pseudo-Hamiltonian systems represent a very large class of interesting dynamic systems, and this approach is a powerful tool. Particularly, a generalization of the Krasovskii’s Theorem is obtained. Then the problem of $L_2$ disturbance attenuation of a nonlinear system via pseudo-Hamiltonian realization is investigated. It is shown that for a class of pseudo-Hamiltonian systems the disturbance attenuation problem is solvable and an estimation of the boundary of the $L_2$ gain is obtained. Finally the results are applied to the excitation control of power systems. The stabilization and the $H_{\infty}$ control problems are investigated for the single-machine infinite bus power systems.


Hamiltonian system, dissipative system, stabilization, disturbance attenuation, power system

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