In this paper, sufficient conditions to ensure the existence of a switching law that makes the solutions of switched Takagi-Sugeno (TS) fuzzy systems ultimately bounded are developed by means of linear matrix inequalities (LMIs). These LMIs are based on the existence of a scalar function, which plays a role similar to Lyapunov energy functions for an auxiliary system formed by a convex combination of all subsystems of the switched system. A feature of the developed results is that the derivatives of the scalar function can assume positive values in a bounded set described as level sets. The LMIs explore the S-procedure to obtain low levels of conservativeness and do not require the calculation of the derivative of the membership functions, which facilitates their application to switched TS fuzzy systems with many rules. Exploring the proposed conditions, we estimated the attractor and basin of attraction of some examples of switched TS fuzzy systems under a measurable switching law. These numerical examples showed the effectiveness of the proposed approach in maximizing the estimation of the bounded attraction domain.

在本文中，通过线性矩阵不等式 (LMI) 开发了确保切换律存在的充分条件，该切换律使切换的 Takagi-Sugeno (TS) 模糊系统的解最终有界。这些 LMI 是基于标量函数的存在，对于由切换系统的所有子系统的凸组合形成的辅助系统，标量函数起着类似于李雅普诺夫能量函数的作用。开发结果的一个特征是标量函数的导数可以在描述为水平集的有界集合中假定为正值。LMI 探索 S 过程以获得低水平的保守性，并且不需要计算隶属函数的导数，这有助于将它们应用于具有许多规则的切换 TS 模糊系统。探索所提出的条件，我们在可测量的切换律下估计了一些切换 TS 模糊系统示例的吸引子和吸引盆。这些数值例子表明了所提出的方法在最大化有界吸引域的估计方面的有效性。