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This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures.

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This article proposes an integral sliding mode control scheme for a class of uncertain nonlinear singular fractional-order systems subject to actuator faults. The interval type-2 Takagi–Sugeno model is used to represent the singular fractional-order systems. First, a novel integral sliding surface is constructed. A sufficient condition is given in terms of linear matrix inequalities which guarantees the admissibility and the robustness of the singular fractional-order systems against actuator faults. Then, aiming at the fault information which is difficult to get in the practical application, an adaptive estimation of fault information is proposed to update the sliding mode controller. A sliding mode fault tolerant control law is designed to make the singular fractional-order systems reach the sliding surface in a finite time. At last, the applicability and effectiveness of the proposed method is illustrated by a numerical simulation example.