Solvability of time-varying infinite-dimensional linear port-Hamiltonian systems

TL;DR

This paper extends the understanding of solvability for infinite-dimensional, time-varying port-Hamiltonian systems, including those with delays, broadening the class of systems for which well-posedness can be established.

Contribution

It generalizes previous results by addressing solvability of infinite-dimensional, time-varying port-Hamiltonian systems beyond boundary control types.

Findings

Established solvability conditions for a broader class of systems.

Illustrated theory with a delay-including port-Hamiltonian system.

Extended the applicability of port-Hamiltonian system analysis.

Abstract

Thirty years after the introduction of port-Hamiltonian systems, interest in this system class still remains high among systems and control researchers. Very recently, Jacob and Laasri obtained strong results on the solvability and well-posedness of time-varying linear port-Hamil\-to\-nian systems with boundary control and boundary observation. In this paper, we complement their results by discussing the solvability of linear, infinite-dimensional time-varying port-Hamiltonian systems not necessarily of boundary control type. The theory is illustrated on a system with a delay component in the state dynamics.