Finite time stabilization of nonlinear singular systems

This paper considers the problems of finite time stability and stabilization for nonlinear singular systems. First, the Lyapunov direct method and the existing results are extended to study the finite time stability of nonlinear singular systems, some sufficient conditions are given and the estimations of settling times are also derived. Then, a finite time control law for nonlinear singular systems is designed by using the extension of control Lyapunov function. Moreover, the continuity of the control law is also discussed by using the extension of small control property. Finally, a numerical example is provided to show the effectiveness of the proposed method.