Stability analysis of singular time-delay systems using the auxiliary function-based double integral inequalities

Thi Hiep Luu and Phan Thanh Nam

International Journal of Systems Science, 2021, vol. 52, issue 9, 1868-1881

Abstract: Recently, there have been a few developments reported on using the Wirtinger/free-matrix-based single integral inequality to stability problem of singular time-delay systems but there has been no report on the double ones. This paper presents an extension on applying the auxiliary function-based double integral inequality to the problem. Furthermore, an extension of the delay-dependent matrix technique into the single integral term of the Lyapunov–Krasovskii function to reduce more the conservatism has also been presented. By proposing an extended Lyapunov–Krasovskii functional (LKF) with triple integral terms and three delay-dependent matrices, a new delay-derivative-dependent stability criterion is derived. The effectiveness of the obtained result is illustrated through a numerical example.

Date: 2021
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DOI: 10.1080/00207721.2021.1871983

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