We report that the control of the 'island width growth rate', which is defined as dW/dt, is more efficient than that of the 'island width' for neoclassical tearing mode stabilization using the minimum seeking method. A concept of the minimum island width growth rate seeking method is newly proposed for the real-time feedback control of the neoclassical tearing mode by using electron cyclotron current drive. To evaluate the performance of the proposed concept, predictive feedback control simulations with an integrated numerical system are performed based on two types of minimum seeking controllers; the first is a finite difference method based controller and the second is a sinusoidal perturbation based controller. The results are compared with the minimum 'island width' seeking method. It is revealed that the proposed control concept is less limited in minimum seeking, and more robust and efficient in reducing the misalignment in shorter time scales.