期刊
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
卷 26, 期 18, 页码 4088-4103出版社
WILEY
DOI: 10.1002/rnc.3551
关键词
stability analysis; time-varying delay; integral inequality; orthogonal polynomial
资金
- National Natural Science Foundation of China [61174038, 61374087, 61473151, 61573007]
- Program for Changjiang Scholars and Innovative Research Team in University [IRT13072]
- Priority Academic Program Development of Jiangsu Higher Education Institutions
- Program for New Century Excellent Talents in University [NCET-13-0859]
- Natural Science Fund for Distinguished Young Scholars of Jiangsu Province [BK20150034]
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 (c) 2016 John Wiley & Sons, Ltd.
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