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International Conference on Numerical Computations: Theory and Algorithms

NUMTA 2019: Numerical Computations: Theory and Algorithms pp 271–279Cite as

Conditions of the Stability Preservation Under Discretization of a Class of Nonlinear Time-Delay Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

Abstract

Nonlinear differential systems with nonlinearities satisfying sector constraints and with constant delays are studied. Such systems belong to well-known class of Persidskii-type systems, and they are widely used for modeling automatic control systems and neural networks. With the aid of the Lyapunov direct method and original constructions of Lyapunov–Krasovskii functionals, we derive conditions of the stability preservation under discretization of the considered differential systems. The fulfilment of these conditions guarantees that the zero solutions of the corresponding difference systems are asymptotically stable for arbitrary values of delays. Moreover, estimates of the convergence rate of solutions are obtained. The proposed approaches are used for the stability analysis of a discrete-time model of population dynamics. An example is given to demonstrate the effectiveness of our results.

Supported by the Russian Foundation for Basic Research, project no. 19-01-00146-a.

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Author information

Authors and Affiliations

  1. Saint Petersburg State University, 199034, Saint Petersburg, Russia

    Alexander Yu. Aleksandrov

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  1. Alexander Yu. Aleksandrov
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Correspondence to Alexander Yu. Aleksandrov .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Aleksandrov, A.Y. (2020). Conditions of the Stability Preservation Under Discretization of a Class of Nonlinear Time-Delay Systems. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_20

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  • DOI: https://doi.org/10.1007/978-3-030-40616-5_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-40615-8

  • Online ISBN: 978-3-030-40616-5

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