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Abstract
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.
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Authors (3)
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Łukasz Grzymkowski mgr inż.
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Damian Trofimowicz mgr inż.
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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International Journal of Applied Mathematics and Computer Science
no. 30,
pages 649 - 658,
ISSN: 1641-876X - Language:
- English
- Publication year:
- 2020
- Bibliographic description:
- Grzymkowski Ł., Trofimowicz D., Stefański T.: Stability analysis of interconnected discrete-time fractional-order LTI state-space systems// International Journal of Applied Mathematics and Computer Science -Vol. 30,iss. 4 (2020), s.649-658
- DOI:
- Digital Object Identifier (open in new tab) 10.34768/amcs-2020-0048
- Verified by:
- Gdańsk University of Technology
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