H for Nonlinear Stochastic Systems

Nadav Berman*, Uri Shaked

*Corresponding author for this work

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

9 Scopus citations


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
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)0780379241
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)0743-1546
ISSN (Electronic)2576-2370


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


Dive into the research topics of 'H for Nonlinear Stochastic Systems'. Together they form a unique fingerprint.

Cite this