L. B. Ryashko, “Stabilization of stochastically perturbed nonlinear oscillations”, Avtomat. i Telemekh., 2007, Issue 10,Pages <nobr>155

This article is cited in 1 paper

Stability of Systems

Stabilization of stochastically perturbed nonlinear oscillations

L. B. Ryashko

Ural State University, Ekaterinburg, Russia

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.

PACS: 02.30.Yy, 02.50.Cw

Presented by the member of Editorial Board: A. I. Kibzun

Received: 14.12.2006