Brief Paper Stability analysis of interconnected Hamiltonian systems under time delays

Sufficient conditions are derived for checking whether interconnected port-Hamiltonian systems are stable in the presence of time delays. It is assumed that the time delay parameters are unknown time-varying functions for which the only available information is about the upper bounds on their magnitude and/or variation. The stability conditions proposed here are established by constructing Lyapunov-Krasovskii stability certificates, based on the Hamiltonians of the individual port-Hamiltonian systems. The forms of the Lyapunov-Krasovskii functionals vary according to the information available on the delay parameter. It is shown how different informations on the delay are utilised to construct stability certificates.