Stability analysis for delayed T-S fuzzy systems: A compensation Lyapunov-Krasovskii functional method combined with
Yang Li1, Yong He1, Ying Yang1
1School of Automation, China University of Geosciences, Wuhan 430074, China; Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China; Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan 430074, China.
Abstract:
A compensation Lyapunov-Krasovskii functional (LKF) method combined with free-weighting matrices is presented to analyze the stability of delayed Takagi-Sugeno fuzzy systems. Firstly, the fuzzy LKF containing membership functions is constructed. Then, the compensation LKF method is presented to introduce the common double and triple integral terms to compensate the single and double integral terms related to the membership functions' derivatives, respectively, which arise in the derivative of the fuzzy LKF. Consequently, following the feature of the membership functions' derivatives, the fuzzy zero equations containing free-weighting matrices of integral terms are proposed to improve the relaxation quality in fuzzy integral terms. Resultantly, the stability criteria with less conservativeness are yielded. Moreover, the conservatism is reduced further by establishing the relaxed fuzzy LKF. Finally, the numerical example is employed to verify the merits of the presented method.
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