Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems

TL;DR

This paper introduces families of structure-preserving reduced order models for linear port Hamiltonian systems using moment matching techniques, ensuring system properties are maintained while matching system behaviors at selected points.

Contribution

It develops parameterized families of port Hamiltonian models that match moments and Markov parameters, preserving structure and extending moment matching methods.

Findings

Families of port Hamiltonian models that match moments at finite points.

Parameterizations that preserve port Hamiltonian structure during reduction.

Application to Markov parameter matching for descriptor systems.

Abstract

In this paper we propose a solution to the problem of moment matching with preservation of the port Hamiltonian structure, in the framework of time-domain moment matching. We characterize several families of parameterized port Hamiltonian models that match the moments of a given port Hamiltonian system, at a set of finite interpolation points. We also discuss the problem of Markov parameters matching for linear systems as a moment matching problem for descriptor representations associated to the given system, at zero interpolation points. Solving this problem yields families of parameterized reduced order models that achieve Markov parameter matching. Finally, we apply these results to the port Hamiltonian case, resulting in families of parameterized reduced order port Hamiltonian approximations.