Some results on stabilization of multiple integrators with input saturation

The stabilization problem for multiple integrators with bounded feedback is considered in this paper. By combining the backstepping technique and a series of saturation functions with different saturation levels, a nested-saturation based controller with pre-chosen parameters can be constructed. Different from the existing methods for systems subject to input saturation, the proposed control design does not require applying the commonly used linear transformation to transform the underlying linear system into an upper-triangular form. The novelty of the proposed method lies in that there is no non-increasing restriction on the saturation levels, which will bring much flexibility to control design. Specifically, owing to the relaxation on the saturation levels, the controller thus designed can be used to improve the convergence performance of the closed-loop system. The effectiveness of the derived method is verified by means of numerical simulations for a triple integrators system.