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