This dissertation mainly deals with the extension of the generalized minimum variance control and generalization of the Robbins-Monro-scheme to account for input variance constraint. In order to account for the input variance constraint, the weighted minimum variance control is extended to include rational transfer functions as well as polynomials as the weighting on control input variance so as to guarantee the closed-loop stability in the whole range of the scalar input weighting and to ensure the monotonic property of the controlled output and control input variances with respect to the scalar input weighting. A sufficient condition for monotonic variation and for the stability of the closed-loop system in the whole range of the scalar weighting on control input is derived in the extended weighted minimum variance control. The algebraic criteria is used to determine the unknown weighting polynomials which satisfy the sufficient condition. In addition, Robbins-Monro scheme is generalized to improve the convergence rate and to increase the monitoring capability in on-line adaptation of the scalar input weighting under the time varying external disturbance to satisfy the constraint on input variance. The two schemes are then combined and applied to the vibration control of a hydraulic servo-damper beam system. The experimental and simulation results show that the maximum use of the available input variance is ensured in the presence of time varying external disturbance so as to achieve the good control performance and the effectiveness of the servo-damper system used for the suppression of the beam vibration.