This brief paper investigates the local stabilization for continues-time Takagi–Sugeno fuzzy systems with constant time delay. In order to deal with the time delay, we design a Lyapunov–Krasovskii functional that is dependent on the membership function. Based on the Lyapunov–Krasovskii functional and the analysis of the time derivative of the membership function, less conservative results can be obtained; however, the Lyapunov–Krasovskii functional is designed so complicated that the Lyapunov level set is hard to be measured directly. Alternatively, two sets are obtained to estimate the local stabilization. One set is for the time-varying initial conditions and the other is for the time-invariant initial conditions. The relationship between the two sets are also discussed. In the end, two examples are given to illustrate the effectiveness of the proposed approach.

中文翻译：

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具有时滞的连续时间 Takagi-Sugeno 模糊系统的局部镇定

这篇简短的论文研究了具有恒定时间延迟的连续时间 Takagi-Sugeno 模糊系统的局部稳定性。为了处理时间延迟，我们设计了一个依赖于隶属函数的 Lyapunov-Krasovskii 函数。基于Lyapunov-Krasovskii泛函和隶属度函数的时间导数分析，可以得到不太保守的结果；然而，Lyapunov-Krasovskii 泛函设计得非常复杂，以至于难以直接测量 Lyapunov 水平集。或者，获得两组以估计局部稳定性。一组用于时变初始条件，另一组用于时不变初始条件。还讨论了这两个集合之间的关系。到底，