The Lyapunov-Razumikhin theorem for the conformable fractional system with delay

Narongrit Kaewbanjak; Watcharin Chartbupapan; Kamsing Nonlaopon; Kanit Mukdasai; Narongrit Kaewbanjak; Watcharin Chartbupapan; Kamsing Nonlaopon; Kanit Mukdasai

doi:10.3934/math.2022267

AIMS Mathematics

2022, Volume 7, Issue 3: 4795-4802. doi: 10.3934/math.2022267

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The Lyapunov-Razumikhin theorem for the conformable fractional system with delay

1.
Faculty of Science at Sriracha, Kasetsart University, Sriracha Campus, Chon Buri, 20230, Thailand
2.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

Received: 02 September 2021 Revised: 06 December 2021 Accepted: 17 December 2021 Published: 27 December 2021
MSC : 34K25, 34K40, 37B25, 58K25

This paper explicates the Razumikhin-type uniform stability and a uniform asymptotic stability theorem for the conformable fractional system with delay. Based on a Razumikhin-Lyapunov functional and some inequalities, a delay-dependent asymptotic stability criterion is in the term of a linear matrix inequality (LMI) for the conformable fractional linear system with delay. Moreover, an application of our theorem is illustrated via a numerical example.
- Lyapunov-Razumikhin technique,
- conformable fractional delayed system,
- linear matrix inequality,
- uniform asymptotic stability
Citation: Narongrit Kaewbanjak, Watcharin Chartbupapan, Kamsing Nonlaopon, Kanit Mukdasai. The Lyapunov-Razumikhin theorem for the conformable fractional system with delay[J]. AIMS Mathematics, 2022, 7(3): 4795-4802. doi: 10.3934/math.2022267

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Abstract

This paper explicates the Razumikhin-type uniform stability and a uniform asymptotic stability theorem for the conformable fractional system with delay. Based on a Razumikhin-Lyapunov functional and some inequalities, a delay-dependent asymptotic stability criterion is in the term of a linear matrix inequality (LMI) for the conformable fractional linear system with delay. Moreover, an application of our theorem is illustrated via a numerical example.

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