On the weak control of slowly damped systems : PMM vol. 42, no. 6, 1978. pp. 1000–1005

Asymptotic formulas are obtained which make it possible to derive the first approximation solution of the Riccati matrix algebraic equation of special form. Method is based on Bass' formulas 1] and the theory of perturbations 2], The problem of control of a slowly damped oscillator is investigated in detail. Formulation of the problem in this paper differs substantially from that in 3] (no assumption is made about single-frequency oscillations, and only a stationary system is considered over an infinite time interval).