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Reports (Research Report) Year : 1994

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

Fabien Campillo
Abdoulaye Traore
  • Function : Author

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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Dates and versions

inria-00074278 , version 1 (24-05-2006)

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  • HAL Id : inria-00074278 , version 1

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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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