Abstarct: In this thesis, we introduce a new method that introduced in recent years to control systems of single-delay differential equations and to stabilization them using the Lambert function. In this way, a new method for designing a controller by allocating a eigenvalue is presented, along with several examples. Using this method, one sub-set of eigenvalues can be transferred to a desirable position. For a system that is represented by delay differential equations, the system response is obtained baxsed on the Lambert function and the stability is checked. If the system is not stable, after reviewing the system controlability, a stabilizing feedback is designed by allocating eigenvalues, and finally the closed loop system can be stable. In the following, we determine the time delay interval for the system to remain stable from the Roth-Horwitz criterion, and then we examine the stability criteria of the single-delay system using the linear matrix inequality method. Finally, the stability of linear systems two delays is expressed. In this chapter, we examine two delays of the variable with time at the input and two fixed delay and variable time delay in state variable. In this section, we must define the suitable Lyapunov function for systems with two delay times, and then we show that the created Lyapunov function is Positive definit and also its derivative is Negative definit. To establish these two conditions, linear Matrix Inequalities (LMIs) are created that guarantee the stability of systems with two time delays. In this thesis, we use the linear matrix inequality method to examine asymptotic stability and give example that can be analyzed by MATLAB software.