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

2022/11/19 by Breiten, Tobias, Hinsen, Dorothea, Unger, Benjamin
#Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2211.10687

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.

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