This paper deals with more relaxed designs of discrete-time Takagi-Sugeno fuzzy-model-based observers via two effective technical measures. Different from previous methods of this field, two effective technical measures are developed for obtaining more relaxed results, i.e., 1) A novel ranking-based switching mechanism is proposed by introducing a set of weighted variables so as to make use of the size differences information among normalized fuzzy weighting functions more freely. 2) A new slack variable method is proposed via the introduction of some extended representations for homogenous polynomials, and those major and minor relationships among all normalized fuzzy weighting functions are mapped to sole augmented multiindexed matrix for each homogeneous polynomial. Therefore, two positive results are provided in this paper, i.e., less conservative fuzzy observers can be given as a result of the above effective measures whilst a part of the online computational cost can be transferred to the offline implementation. Finally, two numerical examples are applied to illustrate the effectiveness of our approach.

中文翻译：

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两种有效技术措施的离散时间非线性系统的松弛模糊观测器设计


本文通过两种有效的技术措施，对基于离散时间 Takagi-Sugeno 模糊模型的观测器进行更宽松的设计。与该领域以往的方法不同，为了获得更宽松的结果，提出了两种有效的技术措施，即，1）通过引入一组加权变量以利用大小差异信息，提出一种新颖的基于排名的切换机制更自由地使用归一化模糊加权函数。 2）通过引入齐次多项式的一些扩展表示，提出了一种新的松弛变量方法，并将所有归一化模糊权重函数之间的主次关系映射到每个齐次多项式的唯一增广多索引矩阵。因此，本文提供了两个积极的结果，即，由于上述有效措施，可以给出不太保守的模糊观测器，同时可以将一部分在线计算成本转移到离线实现。最后，应用两个数值例子来说明我们方法的有效性。