Global stabilization of a class of upper-triangular systems using a generalized homogeneous method

This paper considers the problem of using a smooth controller to globally stabilize a class of upper-triangular systems with uncontrollable linearization. The nonlinearities of the systems do not satisfy the conditions imposed in the existing literature. Based on a new constructive Lyapunov function and a generalized homogeneous design, a small controller is recursively designed in a bottom-to-up fashion to globally stabilize the upper-triangular systems.