Stability analysis for time delay systems via a generalized double integral inequality

Junkang Tian; Zerong Ren; Shouming Zhong; Junkang Tian; Zerong Ren; Shouming Zhong

doi:10.3934/math.2020415

AIMS Mathematics

2020, Volume 5, Issue 6: 6448-6456. doi: 10.3934/math.2020415

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Research article

Stability analysis for time delay systems via a generalized double integral inequality

1.
School of Mathematics, Zunyi Normal University, Zunyi, Guizhou 563006, P. R. China
2.
School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, P. R. China

Received: 01 July 2020 Accepted: 11 August 2020 Published: 18 August 2020
MSC : 34D20, 34K20, 34K25

This paper proposes a new stability condition for a class of time delay systems. Firstly, a generalized double integral inequality is obtained. Then, a less conservative stability criterion is proposed by using the double integral inequality and choosing some new Lyapunov-Krasovskii functionals. Finally, two numerical examples are proposed to show the effectiveness of our method.
- time delay systems,
- linear matrix inequality (LMI),
- double integral inequality,
- Lyapunov-Krasovskii functional (LKF)
Citation: Junkang Tian, Zerong Ren, Shouming Zhong. Stability analysis for time delay systems via a generalized double integral inequality[J]. AIMS Mathematics, 2020, 5(6): 6448-6456. doi: 10.3934/math.2020415

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Abstract

This paper proposes a new stability condition for a class of time delay systems. Firstly, a generalized double integral inequality is obtained. Then, a less conservative stability criterion is proposed by using the double integral inequality and choosing some new Lyapunov-Krasovskii functionals. Finally, two numerical examples are proposed to show the effectiveness of our method.

References

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