Feedback stabilization of stochastic nonlinear composite systems
type: Item
instance of: scholarly article
title: Feedback stabilization of stochastic nonlinear composite systems
zbMATH Open document ID: 0807.93066
DOI: 10.1016/0893-9659(94)90111-2
author: A. Ferfera
author: Abderrahman Iggidr
published in: Applied Mathematics Letters
publication date: 1994-08-07T00:00:00Z
review text: The goal of this paper is to extend the result of \textit{A. Saberi}, \textit{P. V. Kokotovic} and \textit{H. J. Sussmann} [SIAM J. Control and Optimization 28, 1491-1503 (1990; Zbl 0719.93071)] to the stochastic system of the form \[ dx_ t= f(x_ t, y_ t)dt+ g(x_ i, y_ t) dw_ t, \qquad dy_ t= (Ay_ t+ Bu)dt, \] where \(g(x,y)= g(x,0)+ H(x,y) Cy\), \(w_ t\) being a standard Wiener process. It is supposed that \(x_ t\equiv 0\) is globally asymptotically stable in probability (G.A.S.P.) for \[ dx_ t= f(x_ t, 0)dt+ g(x_ t, 0)dw_ t. \] With these conditions it is proved that there exists a control \(u\) such that the corresponding closed-loop system is G.A.S.P. too.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 612158
zbMATH Keywords: nonlinear stochastic systems
zbMATH Keywords: feedback
zbMATH Keywords: global stabilization
zbMATH Keywords: asymptotic stability
reviewed by: Vasile Dragan
MaRDI profile type: Publication
full work available at URL: 0893-9659(94)90111-2
OpenAlex ID: W2082707941
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description: scientific article; zbMATH DE number 612158