# Optimal robustness of port-Hamiltonian systems

## TL;DR

This paper develops methods to construct port-Hamiltonian systems with maximal robustness and passivity, providing algorithms for optimal and near-optimal solutions to ensure system passivity and stability.

## Contribution

It introduces a systematic approach to realize the most robust port-Hamiltonian systems from a given transfer function, including algorithms for optimal and suboptimal passive system approximations.

## Key findings

- Maximal passivity radius realized by normalized port-Hamiltonian systems.
- Algorithm for constructing optimal port-Hamiltonian realization via linear matrix inequalities.
- Suboptimal method for approximating the nearest passive system to a non-passive one.

## Abstract

We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to construct this optimal solution. We also consider the problem of finding the nearest passive system to a given non-passive one and provide a simple but suboptimal solution.