Almost Global Stochastic Stability

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.

• Publication year

  2004

• Venue

  SIAM Journal of Control and Optimization

• Publication date

  2004-11-13

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1137/040618850arXiv math/0411311
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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