TY - GEN
T1 - Dissipative linear stochastic hamiltonian systems
AU - Vladimirov, Igor G.
AU - Petersen, Ian R.
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - 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.
AB - 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.
KW - Stochastic Hamiltonian system
KW - energy balance relations
KW - statistically uncertain noise
KW - stochastic robust stability
KW - virial theorem
UR - http://www.scopus.com/inward/record.url?scp=85062399312&partnerID=8YFLogxK
U2 - 10.1109/ANZCC.2018.8606559
DO - 10.1109/ANZCC.2018.8606559
M3 - Conference contribution
T3 - ANZCC 2018 - 2018 Australian and New Zealand Control Conference
SP - 227
EP - 232
BT - ANZCC 2018 - 2018 Australian and New Zealand Control Conference
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Australian and New Zealand Control Conference, ANZCC 2018
Y2 - 7 December 2018 through 8 December 2018
ER -