Stability analysis for Takagi-Sugeno fuzzy systems with a periodically varying delay via a generalized allowable delay set partitioning approach

Recently, researchers have employed a monotone-delay-interval-based Lyapunov-Krasovskii functional (LKF) to investigate the delay-dependent stability of Takagi-Sugeno (T-S) fuzzy systems with a periodically varying delay. However, this method is limited by its looped LKF structure and seems to ignore the benefits of partitioning the allowable delay set. To address this gap, a generalized allowable delay set partitioning approach is introduced, leveraging the definition of the allowable delay set and a region partitioning scheme, to analyze the stability of T-S fuzzy systems with a periodically varying delay. Our approach allows the construction of different LKFs in various partition sets. This flexibility, compared to existing methods, relaxes the structure of LKF construction and enhances the utilization of system state and delay function information. Subsequently, stability criteria, which exhibit a hierarchy, for T-S fuzzy systems with a periodically varying delay are derived. Finally, the efficacy and superiority of the proposed stability criteria are confirmed through two numerical examples and a practical truck-trailer system.