# Lyapunov exponents of controlled SDE's and stabilizability property : Some examples

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^r(A_k+B_k\,K)\,X_t\,\circ\! dW_k(t) \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.
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https://hal.inria.fr/inria-00074278
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Submitted on : Wednesday, May 24, 2006 - 2:55:49 PM
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• HAL Id : inria-00074278, version 1

### Citation

Fabien Campillo, Abdoulaye Traore. Lyapunov exponents of controlled SDE's and stabilizability property : Some examples. [Research Report] RR-2397, INRIA. 1994. ⟨inria-00074278⟩

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