Asymptotic Stability of port-Hamiltonian Systems

TL;DR

This paper characterizes the asymptotic stability of port-Hamiltonian systems using matrix conditions derived from resolvent criteria, extending stability analysis to networks of vibrating strings.

Contribution

It provides a new matrix-based characterization of asymptotic stability for port-Hamiltonian systems, building on recent exponential stability results and structural insights.

Findings

Matrix conditions for asymptotic stability established

Application to stability analysis of vibrating string networks

Extension of resolvent criteria to port-Hamiltonian systems

Abstract

We characterise asymptotic stability of port-Hamiltonian systems by means of matrix conditions using well-known resolvent criteria from $C_0$-semigroup theory. The idea of proof is based on a recent characterisation of exponential stability established in [Trostorff, Waurick, arXiv:2201.10367], which was inspired by a structural observation concerning port-Hamiltonian systems from [Picard et al., arXiv:2106.10937, accepted in SIAM SICON]. We apply the result to study the asymptotic stability of a network of vibrating strings.