The stability interval of the set of linear system

Authors

  • Waldemar Wójcik Lublin University of Technology http://orcid.org/0000-0002-0843-8053
  • Talgat Mazakov 1. Institute of Information and Computational Technologies CS MES RK, 2. Al-Farabi Kazakh National University, Almaty, Kazakhstan
  • Sholpan Jomartova
  • Gulzat Ziyatbekova 1. Institute of Information and Computational Technologies CS MES RK, 2. Al-Farabi Kazakh National University, Almaty, Kazakhstan
  • Nurgul Karymsakova Al-Farabi Kazakh National University, Almaty, Kazakhstan
  • Aisulu Tursynbai Al-Farabi Kazakh National University, Almaty, Kazakhstan

Abstract

The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and Lienard-Shipar interval criteria. Krylov, Leverier, and Leverier-Danilevsky algorithms are implemented for automated construction and analysis of the interval characteristic polynomial. The interval mathematics library was used while developing the software. The stability of the dynamic system described by linear ordinary differential equations is determined and based on the properties of the eigenvalues of the interval characteristic polynomial. On the basis of numerical calculations, the authors compare several methods of constructing the characteristic polynomial. The developed software that implements the introduced interval arithmetic operations can be used in the study of dynamic properties of automatic control systems, energy, economic and other non-linear systems.

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Published

2024-04-19

Issue

Vol. 67 No. 2 (2021)

Section

Applications

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