Stability and passivity for a class of distributed port-Hamiltonian networks

TL;DR

This paper analyzes a class of distributed port-Hamiltonian systems, establishing their exponential stability and power balance, with applications to power networks using transmission line models based on telegraph equations.

Contribution

It introduces stability and passivity results for infinite-dimensional distributed pH systems invariant under Kirchhoff interconnections, with practical application to power networks.

Findings

Proves exponential stability of the class of distributed pH systems.

Derives a power balance equation for classical solutions.

Illustrates results with power network models based on telegraph equations.

Abstract

We consider a class of infinite dimensional (distributed) pH systems which is invariant under Kirchhoff-type interconnections and prove exponential stability and a power balance equation for classical solutions. The results are illustrated for power networks that incorporate distributed transmission line models based on the telegraph equations.