Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay |
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| Authors: | Jun Chen Shengyuan Xu Weimin Chen Baoyong Zhang Qian Ma Yun Zou |
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| Affiliation: | 1. School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu, China;2. School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou, Jiangsu, China;3. School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu, China |
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| Abstract: | Integral inequalities have been widely used in stability analysis for systems with time‐varying delay because they directly produce bounds for integral terms with respect to quadratic functions. This paper presents two general integral inequalities from which almost all of the existing integral inequalities can be obtained, such as Jensen inequality, the Wirtinger‐based inequality, the Bessel–Legendre inequality, the Wirtinger‐based double integral inequality, and the auxiliary function‐based integral inequalities. Based on orthogonal polynomials defined in different inner spaces, various concrete single/multiple integral inequalities are obtained. They can produce more accurate bounds with more orthogonal polynomials considered. To show the effectiveness of the new inequalities, their applications to stability analysis for systems with time‐varying delay are demonstrated with two numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | stability analysis time‐varying delay integral inequality orthogonal polynomial |
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