A link between contractive and dissipative Hamiltonian systems

This paper should be intended as a preliminary work in which we describe a connection between contractive systems and dissipative Hamiltonian dynamics. In particular, we show that it is always possible to obtain from the Jacobian of the autonomous system, given the contraction metric, the structural matrices of a Hamiltonian dynamics. We show how to obtain in closed-form such matrices for stable linear systems, by exploiting a modification of the Jordan block form. We then conclude the paper by analytically performing the analysis on an example of nonlinear contractive system. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)