Abstract
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.
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