In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order $\alpha \in \left(\mathrm{0,1}\right)$. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

在本文中，使用Takagi–Sugeno模糊模型处理分数阶非线性时滞系统基于观测器的控制设计问题 $\alpha \in （\mathrm{0,1}）$。通过应用Lyapunov–Krasovskii方法，建立了基于模糊观测器的控制器来稳定时滞分数阶Takagi–Sugeno模糊模型。而且，通过状态反馈方法以并行分布补偿方法的形式研究了针对所寻址系统的干扰抑制问题。此外，就线性矩阵不等式而言，为状态反馈增益和观察者增益的存在提供了充分的条件。最后，通过两个数值例子对所提出的方法进行了验证。