Abstract: Partial differential equation (PDE)-based control methods are developed for a class of uncertain nonlinear systems with bounded external disturbances and known/unknown time-varying input delay. Inspired by predictor-based delay compensators, a linear transformation is used to relate the control input to a spatially and time-varying function. The transformation allows the input to be expressed in a manner that separates the control into a delayed control and non-delayed control and also facilitates the ability to compensate for the time-varying aspect of the delay with less complex gain conditions than previous robust control approaches. Unlike previous predictor-based approaches, which inherently depend on the system dynamics, an auxiliary error function is introduced to facilitate a robust control structure that does not depend on known dynamics. The designed controller features gains to compensate for the delay and delay derivative independently and further robustness is achieved since the controller does not require exact model knowledge. In Chapter 2, a tracking controller is developed for a second order system with a known time-varying input delay. A novel Lyapunov-Krasovskii functional is used in the Lyapunov based stability analysis to prove uniform ultimate boundedness of the error signals. Chapter 3 and Chapter 4 focus on the development of a tracking controller for a generalized uncertain nonlinear systems with bounded external disturbances and unknown time-varying input delay. In Chapter 3, a nonlinear mapping is used to map the non-compact time domain to a compact spatial domain, and then a neural network (NN) is used to estimate the unknown time-varying input delay. In Chapter 4, an accelerated gradient descent (AGD) based optimization method is demonstrated to estimate the unknown time-varying delay magnitude. Application of input time-delay for flexible system is examined in Chapter 5. Specifically, an aircraft wing dynamics is considered. The NN based estimation scheme developed in Chapter 3 is combined with a boundary control method, to mitigate oscillations in the aircraft wing in Chapter 5. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Partial Differential Equation Based Control of Nonlinear Systems With Input Delays" by Indrasis Chakraborty, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.