H for Nonlinear Stochastic Systems

Nadav Berman, Uri Shaked

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Number of pages6
StatePublished - 2003
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: 9 Dec 200312 Dec 2003

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216


Conference42nd IEEE Conference on Decision and Control
Country/TerritoryUnited States
CityMaui, HI


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