This paper is devoted to the stability and stabilization for Takagi-Sugeno fuzzy systems with time-varying delays. First, an improved matrix inequality is presented to bound both strictly and nonstrictly proper rational functions, which is more general than the existing versions of reciprocally convex lemmas. Second, by suitable operations on parameter-dependent polynomial multiplied by state rate, a couple of novel intermediary-polynomial-based functions (IPFs) are developed in delay-product types. Benefitting from slack matrices of IPFs, a certain degree of flexibility is furnished. More importantly than that, by feat of adjustment of the variable parameter, the resulting conditions will be further endowed with additive freedom, which relaxes the feasible space in a distinctive manner. Third, by utilizing IPFs along with triple integrals, the stability criteria and the controller design approach are derived by some advanced integral inequalities. Resorting to elaborate construction of IPFs, the strengths of bounding techniques are sufficiently exploited, and the information on delay derivative is adequately reflected. Consequently, more desirable performances are achieved, while without excessive computational complexity. Finally, the effectiveness of the proposed methods is verified by numerical examples.

中文翻译：

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基于中间多项式函数的延迟 Takagi__ugeno 模糊系统的稳定性和可加性自由度稳定性


本文致力于研究时变时滞的 Takagi-Sugeno 模糊系统的稳定性和镇定性。首先，提出了一种改进的矩阵不等式来限制严格和非严格适当的有理函数，这比现有版本的互凸引理更通用。其次，通过对参数相关多项式乘以状态率的适当运算，在延迟乘积类型中开发了一些新颖的基于中间多项式的函数（IPF）。受益于 IPF 的松弛矩阵，提供了一定程度的灵活性。更重要的是，通过对可变参数的调整，所得到的条件将进一步被赋予附加自由度，从而以独特的方式放松了可行空间。第三，通过利用 IPF 和三重积分，通过一些高级积分不等式导出稳定性标准和控制器设计方法。通过精心构造IPF，充分发挥了边界技术的优势，并充分体现了延迟导数的信息。因此，实现了更理想的性能，同时没有过多的计算复杂性。最后，通过数值算例验证了所提方法的有效性。