# Interconnections of input-output Hamiltonian systems with dissipation

arXiv: https://arxiv.org/abs/1603.04019 · HTML: https://mlsanity.com/paper/1603.04019/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2016.

## Built on by (most cited first, 2 of 2)

- [Data assimilation and discrepancy modeling with shallow recurrent decoders](https://mlsanity.com/paper/2512.01170/) (2025)
- [Negative Imaginary Neural ODEs: Learning to Control Mechanical Systems with Stability Guarantees](https://mlsanity.com/paper/2504.19497/) (2025)

## Abstract (arXiv)

Recently, negative imaginary and counter-clockwise systems have attracted attention as an interesting class of systems, which is well-motivated by applications. In this paper first the formulation and extension of negative imaginary and counter-clockwise systems as (nonlinear) input-output Hamiltonian systems with dissipation is summarized. Next it is shown how by considering the time-derivative of the outputs a port-Hamiltonian system is obtained, and how this leads to the consideration of alternate passive outputs for port-Hamiltonian systems. Furthermore, a converse result to positive feedback interconnection of input-output Hamiltonian systems with dissipation is obtained, stating that the positive feedback interconnection of two linear systems is an input-output Hamiltonian system with dissipation if and only if the systems themselves are input-output Hamiltonian systems with dissipation. This implies that the Poisson and resistive structure matrices can be redefined in such a way that the interaction between the two systems only takes place via the coupling term in the Hamiltonian of the interconnected system. Subsequently, it is shown how network interconnection of (possibly nonlinear) input-output Hamiltonian systems with dissipation results in another input-output Hamiltonian system with dissipation, and how this leads to a stability analysis of the interconnected system in terms of the Hamiltonians and output mappings of the systems associated to the vertices, as well as the topology of the network.