The problem of input–output stability analysis and stabilisation of discrete Takagi–Sugeno (T–S) fuzzy systems with a time-varying delay via an input–output (I–O) approach is investigated in this paper. Using a three-term approximation-based model, a forward subsystem with three constant delays and a feedback subsystem are presented. Two separate input–output stability criteria have been formulated, using an input–output approach and a scaled small gain theorem: a criterion based on the lifting method, a non-quadratic Lyapunov function, and bounded real lemma, another criterion based on a non-quadratic Lyapunov–krasovskii functional approach. Using this result, the input–output stabilisation problem is resolved through the so-called parallel distributed compensation (PDC) scheme. The conditions obtained are presented in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the advantages and merit of the proposed method.

本文通过输入输出（I-O）方法研究了具有时变延迟的离散高木-菅野（T-S）模糊系统的输入-输出稳定性分析和镇定问题。使用基于三项近似的模型，提出了具有三个恒定延迟的前向子系统和反馈子系统。使用输入输出方法和缩放小增益定理制定了两个独立的输入输出稳定性标准：一个基于提升方法的标准、一个非二次李雅普诺夫函数和有界实引理，另一个基于非二次函数的标准-二次李雅普诺夫-克拉索夫斯基泛函方法。使用该结果，通过所谓的并行分布式补偿 (PDC) 方案解决了输入-输出稳定问题。获得的条件以线性矩阵不等式 (LMI) 的形式表示。提供了三个数值例子来证明所提出方法的优点和优点。