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Stochastic stabilization and destabilization. (English) Zbl 0820.93071
This paper presents generalizations of previous results on the (de)stabilization by noise of systems to the nonlinear case. Continuous- time finite-dimensional nonlinear systems having a certain contractive property are considered and shown to be almost surely asymptotically stabilizable when perturbed by Brownian motion whose intensity can be adjusted. Also, it is shown that any system whose dimension is larger than one can be destabilized in the almost sure sense by proper choice of the intensity of the perturbing Brownian motion.

93E15Stochastic stability
93C10Nonlinear control systems
Full Text: DOI
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