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Almost Global Stochastic Stability

SIAM J. Control Optim. Volume 45, Issue 4, pp. 1297-1313 (January 2006)

Published October 3, 2006
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We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability. The method can be viewed as a dual to Lyapunov's second method for stochastic differential equations and extends the deterministic result of [A. Rantzer, Syst. Control Lett., 42 (2001), pp. 161–168]. The result can also be used in certain cases to find stabilizing controllers for stochastic nonlinear systems using convex optimization. The main technical tool is the theory of stochastic flows of diffeomorphisms. ©2006 Society for Industrial and Applied Mathematics
History: Received November 13, 2004; accepted April 3, 2006; published October 3, 2006
Permalink: http://dx.doi.org/10.1137/040618850

KEYWORDS and AMS

Keywords
AMS Subject Classifications
34F05, 60H10, 93C10, 93D15, 93E15

PUBLICATION DATA

ISSN:
0363-0129 (print)   1095-7138 (online)
Publisher:
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