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 itself
goes back to 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.
