Improved Stability Criteria for Delayed T-S Fuzzy Systems Using an Augmented Zero Equality Approach

This study attempts to develop improved stability criteria with less conservatism for Takagi-Sugeno fuzzy systems with a time-varying delay that is bounded and differentiable. An augmented Lyapunov-Krasovskii functional is constructed by incorporating extensive information about the time-varying delay and its derivative. An auxiliary function-based integral inequality is combined with an extended reciprocally convex matrix inequality to obtain a tighter bound for the functional derivative. Furthermore, Finsler's lemma and an augmented zero equality approach that takes advantage of the interrelationships between augmented vector elements are employed to develop a less conservative delay-dependent stability criterion for the addressed fuzzy systems. The proposed augmented zero equality approach is then integrated into extended Finsler's lemma to enhance the proposed stability criterion, with the dual goals of reducing computational complexity and attaining a larger delay bound. Two numerical examples demonstrate that the established stability criteria are more efficient and less conservative than those in recent literature.