Improve Backstepping Method to GBM

One of the most important phenomenons in some systems is chaos; so control chaotic systems is difficult and shows the abilities of control methods. In this paper, first known chaotic systems, Lorenz equations, was selected as a chaotic system. One of the best control methods that would be used for stabilization this system, was Backstepping. In this paper this method is improved to Generalized Backstepping Method (GBM). This method is called GBM because of its similarity to Backstepping and more applications in systems than it; Backstepping method is used only to strictly feedback systems but GBM expand this class. For this new method, expose a new theorem and its proof and for showing its abilities, control Lorenz equations in two participate sections; stabilization and tracking reference input. Simulations and the class of systems can be controlled by GBM show that new method has not only more abilities to receive best results than previous method but also apply to control more systems than it.