Stabilization of delayed fractional‐order T‐S fuzzy systems with input saturations and system uncertainties

Abstract

AbstractBy adopting the Takagi–Sugeno (T‐S) fuzzy theory, this paper focuses on the adaptive control of fractional‐order time‐delay systems involving unknown parameters and input saturations. T‐S fuzzy systems with “IF‐THEN” rules are employed to describe fractional‐order nonlinear systems. The influence of input saturation is handled by designing an auxiliary system. By using a norm conversion, the system's time‐delay term is converted into a non‐delayed form. Adaptive updating rules are devised to evaluate uncertainties of the system, and a new control approach is proposed. The devised controller can not only guarantee the boundedness of variables involved but also make state variables converge into a sufficiently small neighborhood of the origin, even in the presence of uncertainties, saturation functions, and system parameters. Finally, numerical studies are given to verify the correctness of the designed scheme.