The present paper aims to analyze the stability of dynamic Interval Type-2 fuzzy control systems (IT2 FCSs) with adjustable parameters by investigating the existence of limit cycles based on the describing function (DF) method. To simplify the stability analysis, the following structured procedure is described. First, to avoid complex computation, a simple architecture of the IT2 FCS using two embedded Type-1 fuzzy control systems (T1 FCSs) is proposed. Then, the DF of IT2 FCS is obtained based on the DFs of embedded T1FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stability regions. Moreover, particle swarm optimization (PSO) technique is utilized to minimize the limit cycle region. Other focus of this paper is on the stability margins analysis for robust design. For this purpose, a gain-phase margin tester is applied to determine the minimum Gain Margin (GM_min) and Phase Margin (PM_min) when limit cycles can arise. Finally, two simulation examples are given to verify the effectiveness of the proposed approach.

中文翻译：

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动态区间2型模糊控制系统的频域稳定性分析

本文旨在通过基于描述函数（DF）方法研究极限环的存在性，分析具有可调参数的动态区间类型2模糊控制系统（IT2 FCS）的稳定性。为了简化稳定性分析，描述了以下结构化程序。首先，为了避免复杂的计算，提出了使用两个嵌入式 Type-1 模糊控制系统 (T1 FCS) 的 IT2 FCS 的简单架构。然后，基于嵌入式 T1FCS 的 DF 获得 IT2 FCS 的 DF。随后，整合稳定性方程和参数平面方法提供了识别极限环和渐近稳定区域的解决方案。此外，利用粒子群优化 (PSO) 技术来最小化极限循环区域。本文的另一个重点是稳健设计的稳定性裕度分析。为此，使用增益相位裕度测试仪来确定最小增益裕度 (G M _{m i n} ) 和相位裕度 ( P M _{m i n} ) 当可能出现极限环时。最后，给出了两个仿真实例来验证所提出方法的有效性。