Sliding Mode Control for Uncertain Fractional-Order Systems with Time-Varying Delays

This article investigates the asymptotic stability of fractional-order (FO) systems with uncertainty and time-varying delay based on the sliding mode control (SMC) method. First, based on the SMC method, a suitable integral type fractional-order sliding mode surface (FOSMS) is designed and the dynamic equations of FO systems under SMC are obtained. Second, by inequality techniques, the condition for asymptotic stability of the FO system has been mathematically established. Then, a novel adaptive SMC law is introduced, which can make sure the accessibility of sliding mode surfaces (SMS). Finally, the feasibility of the results obtained in this paper is verified through a simulation.