Stability and Stabilization of T–S Fuzzy Time-Delay System via Relaxed Integral Inequality and Dynamic Delay Partition

Abstract

This article investigates delay-dependent stability analysis and stabilization for continuous Takagi–Sugeno fuzzy systems with a time-varying delay. By employing dynamic delay partition, the delay interval <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[0, d(t)]$</tex-math></inline-formula> is partitioned into some variable subintervals so that much more information of time-varying delay can be utilized. Moreover, a novel relaxed integral inequality is applied to estimate the derivative of Lyapunov–Krasovskii functionals for achieving reduction of estimation gap. As a result, several further robust stability and stabilization criteria with less conservativeness are proposed. Finally, three examples are provided to demonstrate the effectiveness and advantages of the presented methods.