Mean square stability and stabilization for stochastic nonlinear oscillations

Abstract

An exponential mean square stability for the limit cycles of nonlinear stochastic systems is considered. The first approximation linear systems are introduced and a notion of P-stability (projective) is proposed. A spectral criterion for P-stability is obtained. Mean square stabilization of periodic solutions of stochastically forced nonlinear systems is considered. The necessary and sufficient conditions of stabilizability are presented. The possibilities of constructive design of stabilizing regulator for 2D limit cycles are demonstrated.