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

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.