@inproceedings{4f98dd4c29bc400494335741a1e6054f,
title = "Dissipative linear stochastic hamiltonian systems",
abstract = "This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified by a Hamiltonian, viscous damping parameters and system-environment coupling functions. We consider energy balance relations for such systems with an emphasis on linear stochastic Hamiltonian (LSH) systems with quadratic Hamiltonians and linear coupling. For LSH systems, we also discuss stability conditions, the structure of the invariant measure and its relation with stochastic versions of the virial theorem. Using Lyapunov functions, organised as deformed Hamiltonians, dissipation relations are also considered for LSH systems driven by statistically uncertain external forces. An application of these results to feedback connections of LSH systems is outlined.",
keywords = "Stochastic Hamiltonian system, energy balance relations, statistically uncertain noise, stochastic robust stability, virial theorem",
author = "Vladimirov, \{Igor G.\} and Petersen, \{Ian R.\}",
note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 2018 Australian and New Zealand Control Conference, ANZCC 2018 ; Conference date: 07-12-2018 Through 08-12-2018",
year = "2018",
month = jul,
day = "2",
doi = "10.1109/ANZCC.2018.8606559",
language = "English",
series = "ANZCC 2018 - 2018 Australian and New Zealand Control Conference",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "227--232",
booktitle = "ANZCC 2018 - 2018 Australian and New Zealand Control Conference",
address = "United States",
}