Prescribed-time Stabilization for a Class of Nonlinear Systems with Control Singularities

This paper studies the prescribed-time stabilization of a class of nonlinear systems with control singularities. The settling time is independent of not only the design parameters but also the initial conditions, and can be set according to per our will. By using backstepping, we simultaneously construct a control Lyapunov function (CLF) with singularity and a control law to prescribed-time stabilize the equilibrium point of the studied system in settling time, and avoid all trajectories from crossing the control singularity set. Further, the feasibility region is consistent with the attraction region, and the attraction region is also maximized. That is, the positive invariance condition is achieved. Finally, two examples are presented to illustrate the effectiveness of our proposed method.