In this paper, a discrete-time neural network for solving convex quadratic programming (QP) problems in constrained model predictive control (MPC) technology is investigated and implemented on a digital signal processor (DSP) device. This makes it possible to apply MPC technology to local control for high-dimensional multiple-input-multiple-output systems. The convergence issue of the discrete-time neural network is first studied. By choosing a proper error function, a sufficient condition is obtained under which the neural network converges to the exact optimal solution globally. This is the theoretical basis of this paper. An integrated hardware and software design method to implement the neural network on a DSP chip as a universal QP solver is then developed. With the QP solver handling the computational tasks in MPC problems, a general DSP-based MPC controller is achieved. A prototype system is built on a TMDSEVM6678L DSP development board. It is then applied to an air-separation-unit system and achieves satisfactory control performance. This verifies the effectiveness of the whole design.