# Lyapunov exponents of controlled SDEs and stabilizability property : Some examples

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1 MEFISTO CRISAM - Inria Sophia Antipolis - Méditerranée

Abstract : We consider a stochastic differential equation with linear feedback control~: \begindisplaymath dX t = A+B\,K\,X t\, dt + \sum k=1^rA k+B k\,K\,X t\,\circ\! dW kt \enddisplaymath where $K$ is the feedback gain matrix. For each value of $K$, let $\lambda K$ be the Lyapunov exponent associated with the solution of the SDE. The set of $\lambda K$, as $K$ describe the set of matrices, is a connected interval of $\R$. We present some examples where $-\infty$ is the lower bound of this set. For these cases, we say that the corresponding EDS is stabilizable.

keyword : STOCHASTIC DIFFERENTIAL EQUATION STABILIZABILITY LYAPUNOV EXPONENT

Autor: Fabien Campillo - Abdoulaye Traore -

Fuente: https://hal.archives-ouvertes.fr/

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