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Abstract

This paper gives the simple algorithm for calculation of the degree and coefficients of the minimal polynomial for the complex matrix A = [aij]n x n .

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Authors and Affiliations

S. Białas
M. Białas
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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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Authors and Affiliations

Talgat Mazakov
1
Waldemar Wójcik
2
Sholpan Jomartova
1
Nurgul Karymsakova
3
Gulzat Ziyatbekova
1
Aisulu Tursynbai
3

  1. Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Almaty, Kazakhstan
  2. Lublin Technical University, Poland
  3. Al-Farabi Kazakh National University, Almaty, Kazakhstan

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