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. 683-691. ISSN 0018-9286

## 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 |

Related URLs: | |

Depositing user: | Mrs Carolynne Westwood |

Date Deposited: | 11 Jan 2010 14:19 |

Last modified: | 04 Sep 2014 23:41 |

URI: | http://strathprints.strath.ac.uk/id/eprint/13807 |
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