Robust port-Hamiltonian representations of passive systems

TL;DR

This paper investigates the robustness of port-Hamiltonian representations of passive systems, analyzing how different coordinate choices affect stability and passivity measures through eigenvalue-based quality functions.

Contribution

It introduces robustness measures for port-Hamiltonian representations and relates them to the eigenvalues of the LMI solution set, especially focusing on the analytic center.

Findings

Derived inequalities for passivity radius based on eigenvalue analysis.

Connected robustness of representations to the eigenvalues of the LMI.

Provided insights into the non-uniqueness and stability of port-Hamiltonian forms.

Abstract

We discuss the problem of robust representations of stable and passive transfer functions in particular coordinate systems, and focus in particular on the so-called port-Hamiltonian representations. Such representations are typically far from unique and the degrees of freedom are related to the solution set of the so-called Kalman-Yakubovich-Popov linear matrix inequality (LMI). In this paper we analyze robustness measures for the different possible representations and relate it to quality functions defined in terms of the eigenvalues of the matrix associated with the LMI. In particular, we look at the analytic center of this LMI. From this, we then derive inequalities for the passivity radius of the given model representation.