Global Finite-Time Stabilization for a Chain of Integrators in the Presence of Actuator Saturation by Homogeneous Feedback

This paper considers the problem of globally stabilizing a chain of integrators with actuator saturation in finite time. The proposed method is adapted from an existing scheduled low gain approach by relaxing the range of the value of the low gain parameter. Due to the special structure of the considered system, the proposed feedback law not only results in finite-time stability but also is homogeneous in the whole state space. The homogeneity of the proposed feedback law allows its implementation through the discretization of a compact set of the state space and thus obviation from numerical difficulties in the existing scheduled low gain design. A numerical example is presented to validate our theoretical results and demonstrate that our approach achieves faster convergence than the existing methods.