An optimal strategy is derived for robust performance of feedforward and feedback noise controllers in active noise control systems with a bounded narrowband disturbance. The designed recursive algorithm updates the weighting factor to make sure that controller updates are performed when the current measurement data contain new information to improve the estimation quality. This significantly reduces the computational complexity by allowing fewer updates in the steady state and persistent updates otherwise. The presented algorithm can guarantee non-increasing and positive-definite covariance matrices for feedforward and feedback filters, and this results in a bounded and non-increasing estimation error. Moreover, the proposed algorithm achieves fast convergence with improved performance in steady-state noise reduction. In simulations, the comparison of the proposed method with the established methods under benchmark conditions demonstrates the improvement in the overall performance.