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Stability of Singularly Perturbed Systems with Delay on Homogeneous Time Scales

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Advanced, Contemporary Control

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1196))

Abstract

Conditions for the exponential stability of a linear singularly perturbed system with the small parameter defined on homogeneous time scales are presented. To this aim given system is decomposed onto two subsystems of smaller dimensions than the original one, i.e. onto slow and fast subsystems. It is shown that exponential stability conditions for the system do not depend on small parameter.

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Notes

  1. 1.

    For the purpose of these studies, we use a different notation than the standard in the time scales theory, namely the (forward) graininess function is denoted as \(\kappa \) instead of the standard used \(\mu \). \(\mu \) later on will serve as a parameter.

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Acknowledgement

The work of Olga Tsekhan was partially supported under the state research program “Convergence-2020” of Republic of Belarus: Task 1.3.02. The work of Ewa Pawluszewicz was supported by grant No. WZ/WM/1/2019 of Bialystok University of Technology, financed by Polish Ministry of Science and Higher Education.

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Authors and Affiliations

  1. Bialystok University of Technology, Bialystok, Poland

    Ewa Pawluszewicz

  2. Yanka Kupala State University of Grodno, Grodno, Belarus

    Olga Tsekhan

Authors
  1. Ewa Pawluszewicz
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  2. Olga Tsekhan
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Corresponding author

Correspondence to Ewa Pawluszewicz .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Andrzej Bartoszewicz

  2. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Jacek Kabziński

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Pawluszewicz, E., Tsekhan, O. (2020). Stability of Singularly Perturbed Systems with Delay on Homogeneous Time Scales. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_2

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