Robust stabilization for the chain of integrators with a delay in the input

This paper addresses the robust stabilization of a chain of integrators with a delay and an additive perturbation in the input. A saturated control in an additive form is presented to guarantee that all states have explicit bounds in finite time, and that the closed-loop system is globally asymptotically stable when perturbation does not exist. In principle, the design in this paper admits arbitrarily large time delay and perturbation. In addition, as for the stabilization in the unperturbed case is concerned, the proposed design admits a larger time delay than the existing nested method when the order of the chain of integrators is high. The effectiveness of the algorithm is illustrated by the simulations of a second-order chain of integrators.