Representing the dissipation of infinite-dimensional linear port-Hamiltonian systems

TL;DR

This paper investigates conditions under which infinite-dimensional linear port-Hamiltonian systems can be represented with an energy balance involving a dissipation term dependent on the state, extending finite-dimensional results.

Contribution

It provides a characterization of when infinite-dimensional linear port-Hamiltonian systems admit an energy balance with state-dependent dissipation.

Findings

Identifies conditions for energy balance representation in infinite dimensions

Extends finite-dimensional dissipation concepts to infinite-dimensional systems

Clarifies the structure of dissipation in infinite-dimensional port-Hamiltonian systems

Abstract

It is well known that linear and non-linear dissipative port-Hamiltonian systems in finite dimensions admit an energy balance, relating the energy increase in the system with the supplied energy and the dissipated energy. The integrand in the dissipation term is then a function of the state variable. In this note, we answer the question of when this is possible for linear port-Hamiltonian systems in infinite dimensions.