Vibrational control in H_infinity problems

We consider the application of the theory of vibrational control to H_infinity-problems. We study the possibility of introduction of high-frequency parametric vibrations in order to decrease the minimal attainable value of the H_infinity-norm. We prove the existence of the stabilizing solution of the Riccati equation with quickly oscillating coefficients. This solution is found using the averaging technique as a series of the small parameter.