TY - GEN
T1 - H∞ filtering for nonlinear stochastic systems
AU - Berman, Nadav
AU - Shaked, Uri
PY - 2005
Y1 - 2005
N2 - In this paper we develop an H∞ filtering theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we use 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. We first establish a connection between what is called the L 2-gain property and the solution to a certain Hamilton-Jacobi inequalities (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The infinite time horizon is also considered, where for this case we synthesize a worst case based stable filter which operates on the observation. Stability in this case is taken to be both in the mean-square sense and in probability. The problem of robust filtering 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 an H∞ filtering theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we use 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. We first establish a connection between what is called the L 2-gain property and the solution to a certain Hamilton-Jacobi inequalities (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The infinite time horizon is also considered, where for this case we synthesize a worst case based stable filter which operates on the observation. Stability in this case is taken to be both in the mean-square sense and in probability. The problem of robust filtering 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=33745202638&partnerID=8YFLogxK
U2 - 10.1109/.2005.1467108
DO - 10.1109/.2005.1467108
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AN - SCOPUS:33745202638
SN - 0780389360
SN - 9780780389366
T3 - Proceedings of the 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the 13th Mediterranean Conference on Control and Automation, MED '05
SP - 749
EP - 754
BT - Proceedings of the 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the 13th Mediterranean Conference on Control and Automation, MED '05
T2 - 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the13th Mediterranean Conference on Control and Automation, MED '05
Y2 - 27 June 2005 through 29 June 2005
ER -