Stability analysis of interconnected discrete-time fractional-order LTI state-space systems

• Autorzy: Grzymkowski Łukasz , Trofimowicz Damian , Stefański Tomasz P.

Identyfikatory

DOI

10.34768/amcs-2020-0048

• Języki publikacji: EN

Abstrakty

EN

In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained theoretical results lead to a numerical test for stability evaluation of interconnected FO systems. It is based on modern root-finding techniques on the complex plane employing triangulation of the unit circle and Cauchy’s argument principle. The developed numerical test is simple, intuitive and can be applied to a variety of systems. Furthermore, because it evaluates the function related to the characteristic equation on the complex plane, it does not require computation of state-matrix eigenvalues. The obtained numerical results confirm the efficiency of the developed test for the stability analysis of interconnected discrete-time FO LTI state-space systems.

Słowa kluczowe

EN

stability analysis; discrete time system; fractional order system

PL

analiza stabilności; układ czasu dyskretnego; układ rzędu ułamkowego

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 4
• Strony: 649--658
• Opis fizyczny: Bibliogr. 29 poz., rys., wykr.

Twórcy

autor

Grzymkowski Łukasz

• Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland

autor

Trofimowicz Damian

• Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland

autor

Stefański Tomasz P.

• Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland

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