Geodesic
Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
International Journal of Applied Mathematics and Computer Science, Tome 30 (2020) no. 4, pp. 649-658.

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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.
Keywords: stability analysis, discrete time system, fractional order system
Mots-clés : analiza stabilności, układ czasu dyskretnego, układ rzędu ułamkowego 
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Grzymkowski, Łukasz; Trofimowicz, Damian; Stefański, Tomasz P. Stability analysis of interconnected discrete-time fractional-order LTI state-space systems. International Journal of Applied Mathematics and Computer Science, Tome 30 (2020) no. 4, pp. 649-658. http://geodesic.mathdoc.fr/item/IJAMCS_2020_30_4_a3/

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