TY - GEN
T1 - H∞ for Nonlinear Stochastic Systems
AU - Berman, Nadav
AU - Shaked, Uri
PY - 2003/1/1
Y1 - 2003/1/1
N2 - In this paper we develop a H∞ type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L2-gain property and the solution to a certain Hamilton-Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state-feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.
AB - In this paper we develop a H∞ type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L2-gain property and the solution to a certain Hamilton-Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state-feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.
UR - http://www.scopus.com/inward/record.url?scp=1542379899&partnerID=8YFLogxK
U2 - 10.1109/CDC.2003.1272429
DO - 10.1109/CDC.2003.1272429
M3 - Conference contribution
AN - SCOPUS:1542379899
SN - 0780379241
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5025
EP - 5030
BT - Proceedings of the IEEE Conference on Decision and Control
PB - Institute of Electrical and Electronics Engineers
T2 - 42nd IEEE Conference on Decision and Control
Y2 - 9 December 2003 through 12 December 2003
ER -