A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems
This paper focuses on the delay-dependent stability problem of time-varying delay systems. A generalized free-matrix-based integral inequality (GFMBII) is presented. This inequality is able to deal with time-varying delay systems without using the reciprocal convexity lemma. It overcomes the drawbac...
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| Published in: | Applied mathematics and computation Vol. 354; pp. 1 - 8 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Inc
01.08.2019
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | This paper focuses on the delay-dependent stability problem of time-varying delay systems. A generalized free-matrix-based integral inequality (GFMBII) is presented. This inequality is able to deal with time-varying delay systems without using the reciprocal convexity lemma. It overcomes the drawback that the Bessel–Legendre inequality is inconvenient to cope with a time-varying delay system as the resultant bound contains a reciprocal convexity. Through the use of the derived inequality and by constructing a suitable Lyapunov–Krasovskii function (LKF), improved stability criteria are presented in the form of linear matrix inequalities (LMIs). Two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature. |
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| AbstractList | This paper focuses on the delay-dependent stability problem of time-varying delay systems. A generalized free-matrix-based integral inequality (GFMBII) is presented. This inequality is able to deal with time-varying delay systems without using the reciprocal convexity lemma. It overcomes the drawback that the Bessel–Legendre inequality is inconvenient to cope with a time-varying delay system as the resultant bound contains a reciprocal convexity. Through the use of the derived inequality and by constructing a suitable Lyapunov–Krasovskii function (LKF), improved stability criteria are presented in the form of linear matrix inequalities (LMIs). Two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature. |
| Author | Wang, Wei Zeng, Hong-Bing Liu, Xiao-Gui |
| Author_xml | – sequence: 1 givenname: Hong-Bing orcidid: 0000-0002-0226-2405 surname: Zeng fullname: Zeng, Hong-Bing email: 9804zhb@163.com organization: Department of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China – sequence: 2 givenname: Xiao-Gui surname: Liu fullname: Liu, Xiao-Gui email: 405319366@qq.com organization: Department of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China – sequence: 3 givenname: Wei surname: Wang fullname: Wang, Wei email: wangwei9804@163.com organization: Department of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China |
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| Keywords | Linear matrix inequality Free-matrix-based integral inequality(FMBII) Stability Time-varying delay |
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