Grzymkowski, Łukasz ; Trofimowicz, Damian ; Stefański, Tomasz P.
Contributor:Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Title:Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
Group publication title: Subject and Keywords:stability analysis ; discrete-time systems ; fractional-order systems
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.
Publisher:Zielona Góra: Uniwersytet Zielonogórski
Date: Resource Type: DOI: Pages: Source:AMCS, volume 30, number 4 (2020) ; click here to follow the link
Language: License CC BY 4.0: Rights: