A geometric framework for discrete time port-Hamiltonian systems

TL;DR

This paper develops a geometric framework for discrete-time port-Hamiltonian systems, extending the continuous-time Dirac structure approach to discrete systems, enabling structure-preserving interconnections in a discrete setting.

Contribution

It introduces a novel geometric formulation for discrete-time port-Hamiltonian systems, adapting Dirac structures to discrete-time interconnections.

Findings

Established a geometric formulation for discrete-time port-Hamiltonian systems.

Derived interconnection properties preserving structure in discrete-time.

Extended continuous-time energy-based models to discrete-time systems.

Abstract

Port-Hamiltonian systems provide an energy-based formulation with a model class that is closed under structure preserving interconnection. For continuous-time systems these interconnections are constructed by geometric objects called Dirac structures. In this paper, we derive this geometric formulation and the interconnection properties for scattering passive discrete-time port-Hamiltonian systems.