Port-Hamiltonian Realizations of Nonminimal Linear Time Invariant Systems

TL;DR

This paper develops numerical methods to construct port-Hamiltonian representations for general linear time-invariant systems, including non-minimal cases and systems with non-invertible feedthrough terms, enabling feasibility analysis and perturbation-based adjustments.

Contribution

It extends port-Hamiltonian characterization methods to non-minimal systems and those with non-invertible feedthrough, providing a practical construction and feasibility detection.

Findings

Successfully identifies infeasible port-Hamiltonian systems.

Allows perturbations to approximate non-port-Hamiltonian systems.

Demonstrates methods with numerical examples.

Abstract

Numerical methods for developing port-Hamiltonian representations of general linear time-invariant systems are studied. The approach extends previous port-Hamiltonian characterizations to include the general non-minimal case and the case where the feedthrough term fails to have an invertible symmetric part. The resulting construction is able to identify infeasibility when the system fails to be port-Hamiltonian, and allows for the incorporation of perturbations in order to arrive at a nearby port-Hamiltonian system. Results are illustrated via numerical examples.