A new T–S fuzzy model based robust output-feedback stabilizing controller for fractional-order systems

By using Takagi–Sugeno (T–S) fuzzy set approach, this paper proposes a robust dynamic output feedback (DOF) control for nonlinear fractional-order systems satisfying $$0<\alpha <1$$ . First, using a Fractional Lyapunov function, the novel DOF controller guarantees the stability of the closed-loop system. The proposed approach allows avoiding appearance of crossing terms between the controller’s and the T–S system’s input matrices leading to easier LMI formulation. Second, a new controller is developed by combining a fuzzy dependent Lyapunov function and some special derivations on the controller parameters. This leads to some sufficient conditions in the form of strict linear matrix inequalities (LMIs). When compared with previous work, the proposed method not only has abilities to handle the fuzzy system with the time-derivatives of the membership functions but also can deal with the parametric uncertainties effectively. Simulation examples are provided to demonstrate the validity of the proposed conditions.