Although manufacturing processes are inherently nonlinear, the vast majority of MPC applications are based on linear dynamic models. By using a linear model and a quadratic objective, the nominal MPC algorithm takes the form of a highly structured convex quadratic program (QP), for which reliable solution algorithms can easily be found. This is important because the solution algorithm must converge reliably to the optimum. Nevertheless, there are cases where nonlinear effects are significant enough to justify the use of nonlinear model predictive control. Using a nonlinear model in model predictive control changes the control problem from a convex quadratic program to a non-convex nonlinear problem, which is much more challenging to solve. In this Thesis, we introduce a model predictive control algorithm for nonlinear discrete-time systems. The systems are composed of a linear constant part perturbed by an additive state-dependent nonlinearity term. The control objective is to design a state-feedback control law that minimizes an infinite horizon cost function within the framework of Linear Matrix Inequalities (LMI). In particular, it is shown that the solution of the optimization problem can stabilize the nonlinear plants. Three extensions, namely, application to systems with input delay, nonlinear output tracking, and output feedback, are followed naturally from the proposed formulation. As a natural extension of RMPC, robust state observation (RSO) is also covered in this thesis. The essential point that distinguishes RSO from conventional state observation is that RSO combines physical state nonlinearity with the robust observer formulation. Finally, in this thesis, several numerical examples are given to illustrate the performance of the controller