In view of a fourth-order integrator chain with higher-order nonlinear terms, a nested saturation controller is proposed for a realization of the global asymptotic stability of the system with an input time delay. The stability analysis can be divided into two stages: saturation degradation analysis and asymptotic stability analysis of desaturated systems. The controller uses planar transformation to construct a standard type, followed by a natural cancellation, thus completing the saturation degradation analysis. Then, an important matrix inequality and Lyapunov theorem are used to complete the asymptotic stability analysis. Finally, the effectiveness of the controller is verified by a simulation experiment of an inertial pendulum system.