Contents Online
Communications in Information and Systems
Volume 2 (2002)
Number 2
Pseudo-Hamiltonian realization and its application
Pages: 91 – 120
DOI: https://dx.doi.org/10.4310/CIS.2002.v2.n2.a1
Authors
Abstract
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.
Keywords
Hamiltonian system, dissipative system, stabilization, disturbance attenuation, power system
Published 1 January 2002