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Controlling oscillator coherence by delayed feedback.

We demonstrate that the coherence of a noisy or chaotic self-sustained oscillator can be efficiently controlled by the delayed feedback. We develop a theory of this effect, considering noisy systems in the Gaussian approximation. We obtain a closed equation system for the phase diffusion constant and the mean frequency of oscillation. For weak feedback and strong noise, the theory is in good agreement with the numerics. We discuss possible applications of the effect for the synchronization control.