# Robust port-Hamiltonian representations of passive systems

arXiv: https://arxiv.org/abs/1801.05018 · HTML: https://mlsanity.com/paper/1801.05018/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2018.

## Built on by (most cited first, 4 of 4)

- [Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces](https://mlsanity.com/paper/2206.02660/) (2022)
- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [Data-driven identification of latent port-Hamiltonian systems](https://mlsanity.com/paper/2408.08185/) (2024)

## Abstract (arXiv)

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.