Abstract
This paper deals with the backstepping method for nonlinear systems, through the view points of optimality and globally stability. Based on the concept of nonlinear Cholesky factorization of the approximated value function for the system, we focus on a value function (solution of Hamilton-Jacobi-Bellman (HJB) equation) and a Lyapunov function. Using a nonlinear Cholesky factorization of the approximated value function for the system, we show that the backstepping method can obtain such properties as optimality and globally stability. Simulations are given.
