This paper deals with the observer-based robust H∞ controller design for the Takagi–Sugeno (T-S) continuous fuzzy systems with uncertainties and external disturbances in the case where the premise variables are not measurable. The main objective of this work is to provide robust stability conditions in terms of relaxed LMIs (Linear Matrix Inequalities) for uncertain and disturbed T-S fuzzy systems with unmeasurable premise variables. Using some matrix transformations and lemmas, sufficient conditions of robust stabilisation are derived in the form of a set of relaxed LMIs guaranteeing an optimal value of the H∞ performance level. The proposed LMI constraints are solved using particle swarm optimisation (PSO) algorithm to obtain the robust controller and observer gains. The proposed method has the advantage of having less predefined parameters against the available methods in the literature. The obtained H∞ control scheme ensures asymptotic stability of the closed-loop system as well as strong disturbance attenuation based on the quadratic Lyapunov function, a fuzzy observer and a fuzzy controller. Two simulation examples are provided to show the effectiveness of the proposed approach.

中文翻译：

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基于观测器的鲁棒 H∞ 控制器设计用于使用粒子群优化的未知前提变量的不确定 Takagi-Sugeno 模糊系统

本文讨论了在前提变量不可测量的情况下，具有不确定性和外部干扰的 Takagi-Sugeno (TS) 连续模糊系统的基于观测器的鲁棒 H∞ 控制器设计。这项工作的主要目标是为具有不可测量前提变量的不确定和受干扰的 TS 模糊系统提供松弛 LMI（线性矩阵不等式）方面的稳健稳定性条件。使用一些矩阵变换和引理，以一组松弛 LMI 的形式推导出稳健稳定的充分条件，以保证 H∞ 性能水平的最佳值。提出的 LMI 约束使用粒子群优化 (PSO) 算法求解，以获得稳健的控制器和观察器增益。与文献中的可用方法相比，所提出的方法具有较少的预定义参数的优点。得到的H∞控制方案基于二次Lyapunov函数、模糊观测器和模糊控制器，保证了闭环系统的渐近稳定性和强扰动衰减。提供了两个仿真例子来证明所提出方法的有效性。