Towards a modeling class for port-Hamiltonian systems with time-delay

TL;DR

This paper extends port-Hamiltonian systems to include time-delay systems, providing a new modeling framework that preserves passivity and interconnection properties, with explicit Lyapunov-Krasovskii functional construction.

Contribution

It introduces a novel class of delay port-Hamiltonian systems, expanding the modeling paradigm to infinite-dimensional systems with delays.

Findings

Delay pH systems are passive.

Delay pH systems are closed under interconnection.

Explicit Lyapunov-Krasovskii functionals are constructed.

Abstract

The framework of port-Hamiltonian (pH) systems is a powerful and broadly applicable modeling paradigm. In this paper, 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.