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New criteria for asymptotic stability of a class of nonlinear real-order time-delay systems

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Abstract

This paper investigates the asymptotic stability of a new class of nonlinear time-varying real-order systems that involve multiple delays. First, we introduce a comparison principle and a new lemma that give an estimation for the bounds between the solutions to any two relative systems. Then, by using the inequalities and comparison methodology, we develop some new mathematical results for the asymptotic stability analysis of the zero solution to such a class of systems. We establish new fractional-order-dependent and delay-dependent, and fractional-order-dependent and delay-independent conditions for the analysis of such a class of systems. At the end, we present three examples and demonstrate that some established criteria are very effective for the analysis and control of such systems.

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Acknowledgements

Bichitra Kumar Lenka thanks Indian Institute of Technology Guwahati, India, for supporting Post-Doctoral research under Grant No: MATH/IPDF/2020-21/BIKL/01. The authors would like to thank the anonymous learned reviewers for their insightful comments which helped improve the manuscript. The Associate Editor and the Editor-in-Chief are profusely thanked for allowing a revision.

Funding

This study supported by Indian Institute of Technology Guwahati (MATH/IPDF/2020-21/BIKL/01)

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  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Bichitra Kumar Lenka & Swaroop Nandan Bora

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  1. Bichitra Kumar Lenka
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  2. Swaroop Nandan Bora
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Both authors contributed to the study conception, design and material preparation. Both authors read and approved the final manuscript.

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Correspondence to Swaroop Nandan Bora.

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Lenka, B.K., Bora, S.N. New criteria for asymptotic stability of a class of nonlinear real-order time-delay systems. Nonlinear Dyn 111, 4469–4484 (2023). https://doi.org/10.1007/s11071-022-08060-8

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