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.