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Stability of Singularly Perturbed Systems with Delay on Homogeneous Time Scales

  • Ewa PawluszewiczEmail author
  • Olga Tsekhan
Conference paper
  • 81 Downloads
Part of the Advances in Intelligent Systems and Computing book series (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.

Keywords

Time scale Exponential stability Slow subsystem Fast subsystem Small parameter 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Bialystok University of TechnologyBialystokPoland
  2. 2.Yanka Kupala State University of GrodnoGrodnoBelarus

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