Lyapunov-Function-Free Backstepping Design with Application to the Lorenz System

In this paper we propose a new version of the backstepping control technique, named Lyapunov-Function-Free, for the stabilization of nonlinear systems expressed in strict feedback form. The main characteristic of this technique, in contrast with classic backstepping, is that it avoids the construction of a Lyapunov function at each iteration for the calculation of the controller. The result is a state feedback law that achieves uniform asymptotic stabilization of the system. Simulation tests and comparisons with other backstepping-based methods are performed to show the effectiveness of the proposed technique.