Continuous feedback stabilization for a class of affine stochastic nonlinear systems

Mohamed Oumoun; Lahcen Maniar; Abdelghafour Atlas

Kybernetika (2020)

  • Volume: 56, Issue: 3, page 500-515
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Oumoun, Mohamed, Maniar, Lahcen, and Atlas, Abdelghafour. "Continuous feedback stabilization for a class of affine stochastic nonlinear systems." Kybernetika 56.3 (2020): 500-515. <http://eudml.org/doc/296951>.

@article{Oumoun2020,
abstract = {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.},
author = {Oumoun, Mohamed, Maniar, Lahcen, Atlas, Abdelghafour},
journal = {Kybernetika},
keywords = {continuous state feedback; control stochastic nonlinear systems; global asymptotic stability in probability},
language = {eng},
number = {3},
pages = {500-515},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Continuous feedback stabilization for a class of affine stochastic nonlinear systems},
url = {http://eudml.org/doc/296951},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Oumoun, Mohamed
AU - Maniar, Lahcen
AU - Atlas, Abdelghafour
TI - Continuous feedback stabilization for a class of affine stochastic nonlinear systems
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 3
SP - 500
EP - 515
AB - 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.
LA - eng
KW - continuous state feedback; control stochastic nonlinear systems; global asymptotic stability in probability
UR - http://eudml.org/doc/296951
ER -

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