Appleby, J. and Mao, X. and Rodkina, A. (2008) Stabilization and destabilization of nonlinear differential equations by noise. IEEE Transactions on Automatic Control, 53 (3). pp. 683691. ISSN 00189286

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Abstract
This paper considers the stabilisation and destabilisa tion by a Brownian noise perturbation which preserves the equilibrium of the ordinary dierential equation x0(t) = f(x(t)). In an extension of earlier work, we lift the restriction that f obeys a global linear bound, and show that when f is locally Lipschitz, a function g can always be found so that the noise perturbation g(X(t)) dB(t) either stabilises an unstable equilibrium, or destabilises a stable equilibrium. When the equilibrium of the deterministic equation is non{hyperbolic, we show that a non{hyperbolic perturbation suffices to change the stability properties of the solution. .
Item type:  Article 

ID code:  13807 
Keywords:  brownian motion, almost sure asymptotic stability, It^o's formula, stabilisation, destabilisation, control systems, Probabilities. Mathematical statistics, Mathematics, Control and Systems Engineering, Computer Science Applications, Electrical and Electronic Engineering 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  11 Jan 2010 14:19 
Last modified:  12 Dec 2015 14:33 
URI:  http://strathprints.strath.ac.uk/id/eprint/13807 
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