Finite time stability analysis for nonlinear fractional order differential systems

The finite time stability of nonlinear fractional order differential systems is investigated in this paper. Two versions of finite time stability of Lyapunov theorem for nonlinear fractional order differential systems are proposed. Based on the fractional order extension of Lyapunov method, the finite time stability problem is studied for nonlinear fractional order differential systems, and several stability results are obtained. Via the fractional Lyapunov method by the class-K functions, some sufficient conditions of finite time stability for nonlinear fractional order differential systems are presented. The main results improve the existing results on the finite time stability of general dynamic systems. An illustrative example is provided to illustrate the main results.