H control for discrete-time nonlinear stochastic systems

Nadav Berman, Uri Shaked

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


In this paper we develop an H-type theory for a large class of discrete-nonlinear stochastic systems. In particular, we establish a bounded real lemma for this case. We introduce the notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems, and utilize it in the derivation of the bounded real lemma. In particular, this bounded real lemma establishes necessary and sufficient conditions, in terms of a certain Hamilton Jacobi Inequality (HJI), for a discrete-time nonlinear stochastic system to be an l 2-gain≤ γ. The time-invariant case is also considered, where in this case the bounded real lemma guarantees necessary and sufficient conditions for the system to be l2-gain≤ γ, by means of a solution to a certain algebraic HJI. Stability, in both the mean square sense and in probabilty, is discussed and a utilization of the Linear Matrix Inequalities (LMIs) technique is made to synthesize a controller that achieves an l2-gain property.

Original languageEnglish
Article numberWeC08.6
Pages (from-to)2578-2583
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 1 Jan 2004
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: 14 Dec 200417 Dec 2004

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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