Abstract: The problem of sliding mode control for fractional differential systems with statedelay is considered. A novel sliding surface is proposed and a controller is designed correspondingly, such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point. And the stability of the proposed control design is discussed.

Key words: sliding mode control, fractional di?erential system, time-delay