Stability conditions of axisymmetric instabilities in tokamaks with a resistive shell and an active feedback control system are examined analytically, assuming a ring-shaped plasma. Using equations of plasma motion and equivalent circuits, the basic properties of the feedback control system are discussed. Above a critical n-index, the fast-growing mode is stabilized; the slow-growing mode is stabilized when the feedback loop gain is larger than the critical value, which is proportional to the n-index. The dependence of the stability condition on the positions and time constants of the shell and the control windings is discussed.