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Energy-Based Lyapunov Functions for Forced Hamiltonian Systems with Dissipation

机译：具有耗散的强迫哈密顿系统的基于能量的Lyapunov函数

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摘要

It is well known that the total energy is a suitable Lyapunov function to study211u001ethe stability of the trivial equilibrium of an isolation standard Hamiltonian 211u001esystem. In many practical instances, however, the system is in interaction with 211u001eits environment through some constant forcing terms. This gives rise to what the 211u001eauthors call forced Hamiltonian systems, for which the equilibria of interest are 211u001enow different from zero. When the system is linear a Lyapunov function can be 211u001eimmediately obtained by simply shifting the coordinates in the total energy. 211u001eHowever, for nonlinear systems there is no guarantee that this incremental energy 211u001eis, no even locally, a Lyapunov function. In this paper the authors propose a 211u001econstructive procedure to modify the total energy function of forced Hamiltonian 211u001esystems with dissipation in order to generate Lyapunov functions for non-zero 211u001eequilibria. A key step in the procedure, which is motivated from energy-balance 211u001econsiderations standard in network modeling of physical systems, is to embed the 211u001esystem into a larger Hamiltonian system for which a series of Casimir functions 211u001ecan be easily constructed.

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