The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions in the literature. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. The paper also includes discussions on the inherent limitations associated with fuzzy Lyapunov approaches. To demonstrate the theoretical results, we provide comprehensive examples that elucidate the core concepts and validate the efficacy of the proposed conditions.

翻译：本文旨在为连续时间Takagi-Sugeno（T-S）模糊系统引入新的局部稳定性条件。这些稳定性条件基于线性矩阵不等式（LMI）与二次型Lyapunov函数的结合。此外，它们整合了原点处隶属函数的信息，并有效利用了原点邻域内非线性系统的线性结构。研究证明，与文献中采用模糊Lyapunov函数的现有方法相比，所提条件具有更低的保守性。进一步地，我们证明了所提方法为T-S模糊系统的局部指数稳定性提供了充要条件。本文还讨论了与模糊Lyapunov方法相关的固有局限性。为验证理论结果，我们提供了详尽的算例以阐明核心概念并验证所提条件的有效性。