Asymptotic Stability of 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.

20 pages, 1 figure; v2: typos removed, referee's comments incorporated, additional chapters 3 and 5, dealing with exponential stability and applying findings to the vibrating strings example; 29 pages, 1 figure