In the first part of this thesis stability robustness for quasi-infinite Receding Horizon Control (RHC) of an uncertain nonlinear system is investigated. A sufficient condition is developed for stability of a general nonlinear RHC system subject to perturbations. The result is further specialized to linear systems. For this case it is demonstrated that the closed-loop system is stable out side a bounded set containing the desired equilibrium point upon satisfaction of an LMI constraint along with a bounded perturbation assumption. The new result is applied for control of a mobile robot system which demonstrates the validity of the approach. In the second part, RHC of an uncertain nonlinear system is considered where the computational time is not negligible. The existing method proposes a solution to deal with non-zero computation time by predicting the states at the next sampling time, which provides the controller with sufficient time to generate the required input signal. This work extends this previous result by applying neighboring extremal paths theory to improve the performance further through the addition of a correction phase to the algorithm. The proposed method is composed of three steps: state prediction, trajectory generation, and trajectory correction. The new approach is applied for control of a mobile robot system, which demonstrates significant performance improvements over the existing method
