基于辅助函数的新型积分不等式

数学理论与应用 ›› 2017, Vol. 37 ›› Issue (1): 57-60.

基于辅助函数的新型积分不等式

刘画¹ ,邱赛兵²

1.麓山国际实验学校,长沙,410006; 2.中南大学数学与统计学院,长沙,410083

出版日期:2017-03-30 发布日期:2020-09-24

A New Auxiliary Function-based Integral Inequality

Liu Hua¹ ,Qiu Sai-Bing²

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

摘要/Abstract

摘要： 积分不等式是研究时滞系统稳定性的一种重要方法.本文通过构造更一般的辅助函数和能量函数,利用函数的正交性,证明了一个新型积分不等式,推广了已有结论.

关键词: 能量函数, 辅助函数, 积分不等式, 正交

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

刘画 , 邱赛兵. 基于辅助函数的新型积分不等式[J]. 数学理论与应用, 2017, 37(1): 57-60.

Liu Hua , Qiu Sai-Bing.

A New Auxiliary Function-based Integral Inequality [J]. Mathematical Theory and Applications, 2017, 37(1): 57-60.