Semi-Global Finite-Time Stabilization of Second-Order Systems With Bounded Control Input

This article addresses the semi-global finite-time stabilization problem for second-order systems with bounded control inputs. First, based on the function <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\textbf{tanh}}\boldsymbol{(\cdot)}$</tex-math></inline-formula>, a bounded controller is developed to stabilize the double-integrator system semi-globally at the origin in finite time, and the saturation level of the control input can be prescribed in advance. In addition, the upper-bound estimate for the closed-loop settling time is provided explicitly. Subsequently, the finite-time stability of the closed-loop system is proved by choosing a proper Lyapunov function. Finally, simulation and experimental results regarding the application to address the position tracking problem for the brushless dc (BLDC) motor validate the effectiveness of the proposed bounded controller.