Toward a Class of Port-Hamiltonian Systems With Time-Delays

The framework of port-Hamiltonian (pH) systems is a powerful and broadly applicable modeling paradigm. In this article, we extend the scope of pH systems to time-delay systems. Our definition of a delay pH system is motivated by investigating the Kalman-Yakubovich-Popov inequality on the corresponding infinite-dimensional operator equation. Moreover, we show that delay pH systems are passive and closed under interconnection. We describe an explicit way to construct a Lyapunov-Krasovskii functional and discuss implications for delayed feedback.