Passivity encoding representations of nonlinear systems

TL;DR

This paper explores the relationship between passivity and encoding representations in nonlinear systems, providing a method to construct port-Hamiltonian models from passive system data.

Contribution

It establishes the equivalence between passivity and passivity encoding feasibility, and introduces a method to build port-Hamiltonian representations from known dynamics and Hamiltonians.

Findings

Proves the equivalence between passivity and encoding feasibility

Provides a constructive method for port-Hamiltonian representation

Enhances modeling tools for passive nonlinear systems

Abstract

Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For this, port-Hamiltonian systems are a prominent approach. Another possibility is writing the system in suitable coordinates. In this paper, we investigate the equivalence between passivity and the feasibility of passivity encoding representations, thereby elaborating upon existing results for port-Hamiltonian systems. Based on our findings, we present a method to construct port-Hamiltonian representations of a passive system if the dynamics and the Hamiltonian are known.