Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations

In this paper, we consider the problem of global stabilization for a class of upper-triangular systems which have unbounded or uncontrollable linearizations around the origin. The explicit formula of the control law is designed in two steps: First, we use the generalized adding a power integrator technique to design a homogeneous controller which locally stabilizes the upper-triangular systems. Then, we integrate a series of nested saturation functions with the homogeneous controller and adjust the saturation level to ensure global asymptotic stability of the closed-loop systems. Owing to the versatility of the generalized adding a power integrator technique, our controller not only can be used to stabilize more general upper-triangular systems by relaxing the current conditions used in existing results, but also is able to lead to a stronger result of finite-time stabilization under appropriate conditions. Copyright (C) 2010 John Wiley & Sons, Ltd.