This paper examines the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premise variable space, the original T-S fuzzy model is equivalently converted into a piecewise-fuzzy system. Then, by employing some staircase functions, the continuous membership functions are approximated by a series of discrete values via which the information of membership functions is brought into the stability analysis to reduce the design conservatism. With piecewise-Lyapunov functions, the approaches to the piecewise-fuzzy state feedback and observer-based output feedback controller design are proposed, respectively, in terms of linear matrix inequalities such that the closed-loop system is asymptotically stable with a prescribed $\mathcal {H}_{\infty }$ performance level. It is shown that the membership functions of the fuzzy model and fuzzy controllers are not necessarily the same, which allows more design flexibility. Finally, two illustrative examples are provided to show the effectiveness of the developed methods.

中文翻译：

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不完全前提匹配下TS模糊系统隶属函数相关控制器的新设计

本文研究了一类离散时间 TS 模糊系统的隶属函数相关控制器设计问题。基于前提变量空间的划分方法，将原TS模糊模型等价转化为分段模糊系统。然后，通过采用一些阶梯函数，用一系列离散值逼近连续隶属函数，将隶属函数的信息引入稳定性分析中，以减少设计的保守性。使用分段李雅普诺夫函数，分别根据线性矩阵不等式提出了分段模糊状态反馈和基于观测器的输出反馈控制器设计方法，使得闭环系统渐近稳定且具有指定的 $\mathcal {H}_{\infty }$ 性能水平。结果表明，模糊模型和模糊控制器的隶属函数不一定相同，这允许更大的设计灵活性。最后，提供了两个说明性示例来展示所开发方法的有效性。