Stochastic Passivity in Stochastic Differential Equations: A Port-Hamiltonian Perspective

TL;DR

This paper extends port-Hamiltonian systems to stochastic differential equations, developing passivity concepts for stochastic systems and analyzing a class of linear stochastic systems as an extension of deterministic PHS.

Contribution

It introduces stochastic passivity concepts for stochastic port-Hamiltonian systems and characterizes these in terms of system parameters, extending deterministic PHS theory.

Findings

Developed passivity concepts for stochastic systems

Characterized stochastic PHS in terms of system parameters

Analyzed linear stochastic systems as stochastic PHS extensions

Abstract

We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role for deterministic PHS, we develop several passivity concepts for stochastic input-state-output systems and characterize these in terms of the parameters of the system. Afterwards, we examine properties of a certain class of linear stochastic systems that can be regarded as an extension of linear deterministic PHS to a stochastic passivity framework.