Geodesic
Continuous feedback stabilization for a class of affine stochastic nonlinear systems
Kybernetika, Tome 56 (2020) no. 3, pp. 500-515.

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We investigate the state feedback stabilization, in the sense of weak solution, of nonlinear stochastic systems when the drift is quadratic in the control and the diffusion term is affine in the control. Based on the generalised stochastic Lyapunov theorem, we derive the necessary conditions and the sufficient conditions, respectively, for the global asymptotic stabilization in probability by a continuous feedback explicitly computed. The interest of this work is that the existing control methods are inapplicable to a lot of systems contained in the class of stochastic systems considered in this paper.
DOI : 10.14736/kyb-2020-3-0500
Classification : 60H10, 93C10, 93D05, 93D15, 93E15
Keywords: continuous state feedback; control stochastic nonlinear systems; global asymptotic stability in probability 
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Oumoun, Mohamed; Maniar, Lahcen; Atlas, Abdelghafour. Continuous feedback stabilization for a class of affine stochastic nonlinear systems. Kybernetika, Tome 56 (2020) no. 3, pp. 500-515. doi : 10.14736/kyb-2020-3-0500. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-3-0500/

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