On the development of generalized Hamiltonian realizations

The problem of energy-based Lyapunov functions has been investigated by several authors. The Lyapunov candidates are chosen from the Hamiltonian functions of generalized Hamiltonian systems. Here a new approach provides a method for solving stabilization problems for controlled Hamiltonian systems. Three kinds of generalized Hamiltonian realization are investigated. The first is the generalized Hamiltonian realization of a dynamic system. As an example, the excitation control system is investigated. The feedback dissipative realization of controlled Hamiltonian systems is then considered. A necessary and sufficient condition for existence of this realization is obtained. Finally, the approximate realization is considered. A normal form result is implemented to provide certain computable conditions