Abstract
A problem of stabilization of stochastic oscillatory modes of nonlinear dynamic system is considered. The solution of this problem rests on the spectral criterion of the exponential mean square (root-mean-square) stability of stochastically perturbed limit cycles. The analysis of the stabilizability reduces to the minimization of the spectral radius of a certain positive operator. The efficient possibilities of the obtained stabilizability criterion are illustrated for the case of the cycle on the plane, where the construction of a stabilizing regulator reduces to the minimization of the quadratic functional.
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Original Russian Text © L.B. Ryashko, 2007, published in Avtomatika i Telemekhanika, 2007, No. 10, pp. 155–165.
This work was supported by the Russian Foundation for Basic Research, project nos. 06-01-00625, 06-08-00396, and no. 07-01-96079-r_ural.