Delay-distribution based stability analysis of time-delayed port-Hamiltonian systems

In this paper, the problem of stability analysis of time-delayed port-Hamiltonian systems with probabilistic time-varying delay has been considered. The time-delay variation range is divided into two sub-intervals. By considering the probability distribution of the time-varying delay between the two sub-intervals and the knowledge of the delay variation range, a novel linear matrix inequality (LMI) based stability condition is derived by defining a Lyapunov-Krasovskii functional. It is illustrated with the help of a numerical example that as the probability of delay taking a small value increases, the upper delay bound increases.