Global Finite‐Time Stabilization of Multiple Integrators System With Input Saturation by Time‐Varying Bounded Controls

This article focuses on the issue of global finite‐time stabilization for multiple integrators system with input saturation. By the parametric Lyapunov equation and the nested saturation approach, a time‐varying bounded control scheme combining constant gain feedback and time‐varying gain feedback is proposed. Two distinct dynamic stages are established by the proposed control scheme. First, the state converges to a desired attraction domain in a finite time using the constant gain feedback. Next, by applying a switched strategy, the time‐varying gain feedback ensures that the system state in the domain tends to zero in a finite time. It is proved that the presented control strategy can make the state of the multiple integrators system tend to zero in a finite time without violating the input saturation constraints. Several numerical simulations are provided to validate the effectiveness of the presented method.