Optimal damping of forced stochastic oscillations in linear systems in the case of unknown spectral density of external disturbance

We present a solution of the new infinite horizon linear-quadratic optimization problem concerning the optimal damping of forced stochastic oscillations. It differs from well-known similar problems mainly in the assumption that there is no full information on the spectral density of the external disturbance and that the spectral density tends rapidly to zero (for example exponentially) as the frequency tends to infinity.