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Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback
Kybernetika, Tome 52 (2016) no. 6, pp. 988-1002 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we give sufficient conditions under which a nonlinear stochastic differential system without unforced dynamics is globally asymptotically stabilizable in probability via time-varying smooth feedback laws. The technique developed to design explicitly the time-varying stabilizers is based on the stochastic Lyapunov technique combined with the strategy used to construct bounded smooth stabilizing feedback laws for passive nonlinear stochastic differential systems. The interest of this work is that the class of stochastic systems considered in this paper contains a lot of systems which cannot be stabilized via time-invariant feedback laws.
In this paper we give sufficient conditions under which a nonlinear stochastic differential system without unforced dynamics is globally asymptotically stabilizable in probability via time-varying smooth feedback laws. The technique developed to design explicitly the time-varying stabilizers is based on the stochastic Lyapunov technique combined with the strategy used to construct bounded smooth stabilizing feedback laws for passive nonlinear stochastic differential systems. The interest of this work is that the class of stochastic systems considered in this paper contains a lot of systems which cannot be stabilized via time-invariant feedback laws.
DOI : 10.14736/kyb-2016-6-0988
Classification : 60H10, 93C10, 93D05, 93D15, 93E15
Keywords: stochastic differential systems; smooth time–varying feedback law; global asymptotic stability in probability 
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     author = {Florchinger, Patrick},
     title = {Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback},
     journal = {Kybernetika},
     pages = {988--1002},
     year = {2016},
     volume = {52},
     number = {6},
     doi = {10.14736/kyb-2016-6-0988},
     mrnumber = {3607858},
     zbl = {06707384},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-6-0988/}
}
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Florchinger, Patrick. Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback. Kybernetika, Tome 52 (2016) no. 6, pp. 988-1002. doi: 10.14736/kyb-2016-6-0988

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