On the Local Quadratic Stability of T-S Fuzzy Systems in the Vicinity of the Origin
This work addresses stability analysis for fuzzy control systems, offering incremental improvements in reducing conservatism for engineers and researchers in control theory.
The paper tackles the problem of local stability for continuous-time Takagi-Sugeno fuzzy systems by introducing new conditions based on linear matrix inequalities and quadratic Lyapunov functions, which are proven to be less conservative and provide necessary and sufficient conditions for local exponential stability.
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.