Finite-time stability of equilibrium point of a class of fractional-order nonlinear systems

This paper studies the finite -time stability (FTS) of equilibrium point of a class of fractionalorder nonlinear systems (FONSs) described by Caputo fractional -order derivative (CFOD). The definition of finite -time equilibrium point (FTEP) is proposed for the FONSs, and it is proved that the CFOD of the FTEP is not constantly equal to 0. A sufficient and necessary condition on the FTEP is proposed. Based on the asymptotical stability and the method of the integral of unbounded integrand, two sufficient conditions on the FTS of the equilibrium point are provided. Consequently, the existence of finite -time stable equilibrium points in the FONSs is confirmed. Two examples are presented to illustrate the proposed results.