Robust control of fractional-order Liu system is addressed in this paper. The proposed approach relies on sliding mode control being established on a novel fractional-order integral type sliding surface. Theoretically, based on classical Lyapunov stability theorem, it has been shown that under suitable conditions, the proposed controller guarantees the system's stability. Further, it is shown that the method presented is capable for both commensurate and incommensurate systems. In order to reduce the chattering effect, a fuzzy logic controller is employed. Numerical simulations verify these results.

Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.