M.Sc.

The main aim of this work is classified into four objects, these are summarized as follows:

The main theme of this thesis is the design of a full order nonlinear deterministic dynamic observer for estimation of state space from its nonlinear input-output dynamic control system.The quadratic Lyapunov function stabilization approach has been adapted and developed.The sufficient conditions for existence of the dynamic observer for some class of nonlinear input-output dynamic system have been presented and discussed. Useful linear transformations have also been adapted to design a stable controller based on the suggested dynamic (deterministic) observer system.

The main aim of this work is to generalize the study of the one-dimensional integral equations to include the multi-dimensional integral equations.This study includes the classification of the multi-dimensional integral and integro-differential equations.Also, some extended theorems for the existence and uniqueness of solution for the multi-dimensional integral equations are given.Moreover, some generalized methods are used to solve the multi-dimensional integral equations, with some illustrative examples