In this paper, we will investigate the problem of finite frequency memory fixed-order output feedback controller design for Takagi–Sugeno (T–S) fuzzy affine systems. It is assumed that the disturbances reside in a finite frequency range, i.e., the low, middle, or high frequency range. The objective is to design a memory piecewise affine (PWA) controller by using past output measurements to guarantee the asymptotic stability of the resulting closed-loop system with a prescribed finite frequency $\mathscr H_{\infty }$ performance. Via the system state-input augmentation, a novel descriptor system approach is proposed to facilitate the controller design. All the design conditions are formulated in the form of linear matrix inequalities. It is also proven that the $\mathscr H_{\infty }$ performance can be improved with the memory control strategy. Finally, simulation studies are presented to show the effectiveness of the proposed design method.

中文翻译：

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TS模糊动力系统的有限频记忆输出反馈控制器设计

在本文中，我们将研究 Takagi-Sugeno (T-S) 模糊仿射系统的有限频率记忆定阶输出反馈控制器设计问题。假设干扰存在于有限的频率范围内，即低频、中频或高频范围。目标是通过使用过去的输出测量来设计内存分段仿射 (PWA) 控制器，以保证最终闭环系统在规定的有限频率下的渐近稳定性$\mathscr H_{\infty }$表现。通过系统状态输入增强，提出了一种新颖的描述符系统方法来促进控制器设计。所有设计条件都以线性矩阵不等式的形式表述。也证明了$\mathscr H_{\infty }$内存控制策略可以提高性能。最后，仿真研究显示了所提出的设计方法的有效性。