Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain: An Introduction

TL;DR

This paper introduces the theory of infinite-dimensional linear port-Hamiltonian systems on a one-dimensional domain, focusing on Dirac structures, well-posedness, stability, and dissipativity, combining operator theory with physical Hamiltonian methods.

Contribution

It provides a comprehensive introduction and new verifiable conditions for well-posedness and stability of these systems, bridging abstract and physical approaches.

Findings

Derived verifiable conditions for well-posedness

Established criteria for stability and dissipativity

Connected operator theory with physical Hamiltonian methods

Abstract

We provide an introduction to infinite-dimensional port-Hamiltonian systems. As this research field is quite rich, we restrict ourselves to the class of infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domainand we will focus on topics such as Dirac structures, well-posedness, stability and stabilizability, Riesz-bases and dissipativity. We combine the abstract operator theoretic approach with the more physical approach based on Hamiltonians. This enables us to derive easy verifiable conditions for well-posedness and stability.