A Finite-time State Feedback Stabilization Method for a Class of Second Order Nonlinear Systems

Abstract

The finite-time feedback stabilization problem of a class of second-order nonlinear systems is discussed. Three kinds of global finite-time feedback stabilization approaches based on continuous state feedback are given. First, using homogeneous properties of nonlinear homogeneous systems, a state feedback controller is designed to guarantee that the closed loop system is asymptotically stable and satisfies negative homogeneity. Sec-ond, using backstepping constructive approach based on finite-time Lyapunov function, a finite-time controller is developed. Finally, using nonsingular terminal sliding mode technology, a feedback stabilizing controller which can make the closed loop system converge to equilibrium in finite time is given. Simu-lation results are provided to demonstrate the effectiveness of these approaches.