Global Finite-Time Stabilization of First-Order Systems With Bounded Controls

This brief addresses the global finite-time stabilization problem for systems with bounded controls. First, based on the bounded functions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\textrm {tanh}}(\cdot)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\textrm {arctan}}(\cdot)$ </tex-math></inline-formula> , two classes of bounded global finite-time controllers are proposed to stabilize single integrator systems and the saturation level of the control input can be prescribed. In addition, for each proposed controller, the upper-bound estimate for closed-loop settling time is provided explicitly, which is closely related to a parameter reflecting the initial state location. Finally, the effectiveness of the proposed controllers is verified through simulation.