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Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback. (English) Zbl 1389.93200
The author derives sufficient conditions which guarantee the global asymptotic stabilization in probability for nonlinear stochastic differential systems without unforced dynamics. This is done with help of a stabilizing time-varying feedback. The main tools are the stochastic Lyapunov stability theory combined with the stochastic LaSalle invariance principle and the bounded feedback design technique for passive stochastic differential systems. Several examples of the systems which cannot be stabilized via time-invariant feedback law are presented.
93D15 Stabilization of systems by feedback
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93C10 Nonlinear systems in control theory
93E15 Stochastic stability in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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