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Generalized compensation functional method to local stability criterion of Takagi-Sugeno fuzzy systems with time-varying delays
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DOI：10.1016/j.fss.2026.110027.png)
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Abstract
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The local stability of Takagi-Sugeno fuzzy systems with time-varying delays is addressed via the generalized compensation functional method. Firstly, the enhanced augmented fuzzy Lyapunov-Krasovskii functional (LKF) is yielded, in which membership functions are contained in the fuzzy quadratic term and fuzzy integral terms. Secondly, the generalized compensation functional method is presented to compensate fuzzy integral terms correlated with the time derivative of membership functions (TDMFs), then fuzzy zero-equations are introduced in the fuzzy quadratic and integral terms to enhance the feasibility. Then, the improved local stability criterion with reduced conservatism is established, where the bounds of TDMFs are expanded and adopted by considering traits of TDMFs. Moreover, when membership functions depend on time, the global stability condition with less conservatism is established, while actual upper and lower bounds of TDMFs are utilized in the criterion. Finally, examples are offered to verify the reduced conservatism of stability criteria.
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