M.Sc.

 
The main purpose of this work may be divided into the following aspects:
1. Study the Chebyshev polynomials of the first and second kinds defined on the intervals [0,1] and [-1,1] and modify some of their properties

2. Use two methods to solve the linear ordinary differential equations with nonconstant coefficients, namely,Chebyshev-matrix method and Chebyshev series method.
3. Devote Chebyshev series method to solve system of linear Fredholm integral
equations and integro-differential equations.

  The main aim of this work is focused on studying the global asymptotic stability in the probability for some class of closed-loop control system of Itotype in the presence of system uncertainty.  Some onlinear continuous-time Ito-dynamic stochastic system deriven by unbounded stochastic noise input have been considered, where the equilibrium point of the stochastic system is preserved even in the presence of noise  The global asymptotic stability in probability has been developed by using stabilization controller and Lyapunov stochastic approach.

The tracking problem for differential stochastic equations in the present of stochastic uncertainty of white noise, and control input have been considered. In this work, our consideration have been focused on the case where both original dynamic state stochastic system and the desired stochastic dynamic system, are driven  by white noise stochastic process. The main aim of this work is to make the behavior of the original dynamic system following the behavior of the desired one for arbitrary controller, using tracking control system approach.