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Generalization of Inequality and Its Application in Additive Time-Varying Delay Systems

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Abstract:

This article mainly studies the improvement problem of integral inequality and applies it to the stability study of additive time-varying delay systems: Firstly, the existing Wirtinger inequality is proven from the perspectives of monotonicity and adding positive terms using the method of constructing parameter functions. Secondly, we propose extended inequalities, including the extended Wirtinger inequality and the extended cross-convex inequality which is based on third-order matrices. Thirdly, utilizing these two extended inequalities, we provide criteria for determining the asymptotic stability of additive time-varying delay systems in the form of Linear Matrix Inequalities (LMIs). Finally, numerical examples are presented to demonstrate the effectiveness and superiority of the proposed method.

Key words: Additive time-varying delay system, Wirtinger inequality, Stability analysis

CLC Number:

O211

Fan Tianjiao, Feng Lichao, Yang Yanmei. Generalization of Inequality and Its Application in Additive Time-Varying Delay Systems[J].Acta mathematica scientia,Series A, 2024, 44(5): 1335-1351.

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