In this article, the homogenous polynomially membership functions dependent (HPMFD) matrices are used to study the interval type-2 Takagi–Sugeno fuzzy systems. First, some necessary notations of the HPMFD matrices are introduced. Next, based on these notations, the time derivative of the HPMFD matrices is discussed and a switching method is proposed to ensure that the time derivative of the HPMFD matrices is negative. Then, a HPMFD controller is designed and new stabilization conditions are obtained by using the HPMFD Lyapunov function. In the end, the simulations show that the method in this article is less conservative than the existing ones in the literatures.

中文翻译：

---

均值多项式隶属函数依赖矩阵和切换技术对区间2型模糊系统的稳定性分析

在本文中，均质多项式隶属函数相关（HPMFD）矩阵用于研究区间2型Takagi-Sugeno模糊系统。首先，介绍了HPMFD矩阵的一些必要符号。接下来，基于这些符号，讨论了HPMFD矩阵的时间导数，并提出了一种切换方法以确保HPMFD矩阵的时间导数为负。然后，设计一个HPMFD控制器，并通过使用HPMFD Lyapunov函数获得新的稳定条件。最后，仿真表明本文所采用的方法不如文献中已有的方法那么保守。