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.