It is vital to have an exclusive modification in the semiconductor production process because of meeting differentiated customer demands in the dynamic and competitive global minuscule semiconductor technology market and the highly complex fabrication process. In this paper, we propose a control system based on the dynamic mixed-effect least-square support vector regression (LS-SVR) control system for overlay error compensation with stochastic metrology delay to minimize the misalignment of the patterning process. Moreover, the novel Lyapunov-based kernel function is merged with the LS-SVR controller for the stability of the control system in the presence of metrology delay and to deal with nonlinearity among the overlay factors. A major semiconductor manufacturer in Taiwan has validated and implemented the proposed controller's operation. The experiments verified that the mixed-effect LS-SVR controller has higher validity and higher efficiency in comparison with the exponentially weighted moving average (EWMA) and threaded EWMA controllers, which had been previously implemented at the company or applied in similar studies.