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The limit cycles of nonlinear systems under the small stochastic disturbances are considered. The random trajec-tories of forced system leave the deterministic cycle and form some stochastic bundle around it. The probabilistic description of this bundle near cycle based on stochastic sensitivity function (SSF) is suggested. The SSF is a covariance matrix… (More)

A nonlinear discrete-time control system forced by stochastic disturbances is considered. We study the problem of synthesis of the regulator which stabilizes an equilibrium of the deterministic system and provides required scattering of random states near this equilibrium for the corresponding stochastic system. Our approach is based on the stochastic… (More)

—We consider a nonlinear discrete-time control system forced by stochastic disturbances. The problem addressed is a design of the feedback regulator that stabilizes an equilibrium of the closed-loop determin-istic system and synthesizes a required dispersion of random states for corresponding stochastic system. To solve this problem we develop a method… (More)

We present a new computer approach to the spatial analysis of stochastically forced 3D-cycles in nonlinear dynamic systems. This approach is based on a stochastic sensitivity analysis and uses the construction of confidence tori. A confidence torus as a simple 3D-model of the stochastic cycle adequately describes its main probabilistic features. We suggest… (More)