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Paper details
Number 4 - December 2020
Volume 30 - 2020
Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
Łukasz Grzymkowski, Damian Trofimowicz, Tomasz P. Stefański
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.
Keywords
stability analysis, discrete-time systems, fractional-order systems