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H-infinity controller design for affine fuzzy systems based on piecewise Lyapunov functions in finite-frequency domain

机译：基于分段Lyapunov函数的有限频域仿射模糊系统H-∞控制器设计

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This paper studies the problem of state feedback controller design for a class of nonlinear systems described by continuous-time affine fuzzy models. Based on a piecewise continuous Lyapunov function combined with S-procedure and some matrix decoupling techniques, a novel control law is derived in the formulation of linear matrix inequalities (LMIs) in finite-frequency domain. First, a so-called finite-frequency H-infinity performance index is defined, which extends the standard H-infinity performance. Then, a sufficient condition is derived such that the fuzzy closed-loop system satisfies a finite-frequency H-infinity performance. By introducing the S-procedure and adding slack variables, piecewise controllers are designed to deal with disturbances in the low-, middle-, and high-frequency domain, respectively. The proposed piecewise controller design method can get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. Finally, two examples are given to illustrate the effectiveness and superiority of the new results. (C) 2015 Elsevier B.V. All rights reserved.
机译：本文研究了用连续时间仿射模糊模型描述的一类非线性系统的状态反馈控制器设计问题。基于分段连续Lyapunov函数，结合S过程和一些矩阵解耦技术，在有限频域中线性矩阵不等式（LMI）的表示中推导了新的控制律。首先，定义了所谓的有限频率H无限性能指标，该指标扩展了标准H无限性能。然后，导出足够的条件，以使模糊闭环系统满足有限频率的H无穷大性能。通过引入S程序并添加松弛变量，设计了分段控制器，分别处理低频，中频和高频域中的干扰。当扰动的频率范围事先已知时，所提出的分段控制器设计方法可以获得更好的扰动衰减性能。最后，给出两个例子来说明新结果的有效性和优越性。 （C）2015 Elsevier B.V.保留所有权利。

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