Improved stability criterion for distributed time-delay systems via a generalized delay partitioning approach

Zerong Ren; Junkang Tian; Zerong Ren; Junkang Tian

doi:10.3934/math.2022740

AIMS Mathematics

2022, Volume 7, Issue 7: 13402-13409. doi: 10.3934/math.2022740

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Research article

Improved stability criterion for distributed time-delay systems via a generalized delay partitioning approach

Zerong Ren ,
Junkang Tian ^,

School of Mathematics, Zunyi Normal University, Zunyi, Guizhou 563006, China

Received: 11 February 2022 Revised: 25 April 2022 Accepted: 10 May 2022 Published: 17 May 2022
MSC : 34D20, 34K20, 34K25

This paper researches the problem of stability analysis for distributed time-delay systems. A newly augmented Lyapunov-Krasovskii functional (LKF) is first introduced via a generalized delay partitioning approach. Then, a less conservative stability criterion is derived by introducing a novel Jensen inequality to estimate the integral terms in the derivative of LKF. The stability condition is given in terms of linear matrix inequality. Finally, the merits of the obtained stability criterion is shown by a well-known example.
- delay partitioning approach,
- linear matrix inequality,
- Lyapunov-Krasovskii functional,
- Jensen inequality
Citation: Zerong Ren, Junkang Tian. Improved stability criterion for distributed time-delay systems via a generalized delay partitioning approach[J]. AIMS Mathematics, 2022, 7(7): 13402-13409. doi: 10.3934/math.2022740

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Abstract

This paper researches the problem of stability analysis for distributed time-delay systems. A newly augmented Lyapunov-Krasovskii functional (LKF) is first introduced via a generalized delay partitioning approach. Then, a less conservative stability criterion is derived by introducing a novel Jensen inequality to estimate the integral terms in the derivative of LKF. The stability condition is given in terms of linear matrix inequality. Finally, the merits of the obtained stability criterion is shown by a well-known example.

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