Global stabilization of a chain of integrators with input saturation and disturbances

In this paper, the problem of global stabilization for a chain of integrators in presence of input saturation and disturbances is solved. A novel and elegant approach to solve this problem, in absence of disturbances, was proposed by Teel [1] using saturation functions and coordinate transformation. With Teel's work as foundation, many results have been proposed to improve the performance of tracking/stabilizing controllers for chain of integrators. However, in presence of disturbances, the coordinate transformation can considerably shrink the region where the controller is unsaturated. In this work, we present a modified backstepping like approach to solve the global stabilization problem which does not rely on coordinate transformation. Comparative studies performed using a third order integrator chain proves the effectiveness of the proposed scheme.