In this project, we focus on the stability theory for system of differential equations, concentrating in particular on the system of first order ordinary differential equations, delay differential equations, the mathematical formulation of time varying wireless networks, where the users of the networks are in relative motion. For both types of system, we provide definitions of the appropriate stability concepts and consider methods whereby one can obtain sufficient conditions for these concepts to apply. In doing this, we investigate in detail the methods of Lyapunov for ordinary differential equation systems. We then investigate the application of some of these methods to an important general class of continuous time algorithms for the control of antenna transmission powers in wireless networks. We showed that in this case if the solution for the power of the system exists, the solution is asymptotically stable. It is also showed that the stability is global this means that for all initial conditions have same asymptotic behaviors.