Quadratic Dynamic Matrix Control (QDMC) with state estimation is presented for use with nonlinear process models. This formulation extends Garcia's nonlinear version of QDMC to open- loop unstable nonlinear processes and allows for better disturbance rejection. It also extends Ricker's linear state space formulation with state estimation to nonlinear systems. Stability and better performance is observed when compared to the algorithm without state estimation in rejecting disturbances for processes operating at unstable steady state setpoints, as illustrated with two simple examples. The algorithm requires that only a Quadratic Program be solved on-line. The modest computational requirements make it attractive for industrial implementation. the effectiveness of the approach is demonstrated by its successful application to the temperature control of a semibatch polymerization reactor. A model and related control requirements for this problem were presented at the 1990 AIChE Annual Meeting in a session on "Industrial Challenge Problems in Process Control."