Mathematical Theory and Applications ›› 2017, Vol. 37 ›› Issue (1): 57-60.

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A New Auxiliary Function-based Integral Inequality

Liu Hua1 ,Qiu Sai-Bing2   

  1. 1.Lushan International Experimental School,Changsha 410006,China; 2.School of Mathematics and Statistics,Central South University,Changsha 410083,China

  • Online:2017-03-30 Published:2020-09-24

Abstract: Integral inequality is an important tool to study the stability of delayed systems.In this paper,a general auxiliary function and a energy function are constructed.Based on the orthogonality of functions,a new integral inequality is derived,which extends the Jensen integral inequality.

Key words: Time-delay system, Auxiliary function, Integral inequality, Orthogonality