Precise attitude and shape control of flexible spacecraft requires active control of flexural vibrations. This paper first derives a general closed loop characteristic equation of a flexural vibration control system equipped with arbitrary numbers of non-point actuators and sensors whose regions of actions and observations are expressed by weight functions. Then, the characteristic equation in a determinantal form is expanded in a mathematically tractable form in which each coefficient is a product of an actuator-dependent determinant, a sensor-dependent determinant and a compensator-dependent determinant. By applying the perturbation technique to the expanded characteristic equation, it is shown that a modal stabilizing condition can be obtained for a rate and position feedback control system. Finally, a numerical example is given to illustrate the usage of the condition.