A Generalized Reciprocally Convex Inequality on Stability and Stabilization for T–S Fuzzy Systems With Time-Varying Delay

This article investigates the stability and stabilization issues of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay via a generalized reciprocally convex inequality (GRCI). The enhanced stability criteria with less conservatism are achieved by employing a novel GRCI and establishing an asymmetric Lyapunov–Krasovskii (L–K). The proposed reciprocally convex method encompasses some previous methods as exceptional examples by introducing a matrix-valued polynomial. Moreover, an asymmetric L–K functional with delay-product terms is proposed for the stability of the T–S fuzzy systems. Then, a stabilization method is produced based on the parallel distributed compensation. Finally, case studies are carried out to indicate the effectiveness and advantages of the stability and stabilization criteria.

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