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

• Main Authors: Grzymkowski Łukasz, Trofimowicz Damian, Stefański Tomasz P.
• Format: Article
• Language: English
• Published: Sciendo 2020-12-01
• Series: International Journal of Applied Mathematics and Computer Science
• Subjects: stability analysis; discrete-time systems; fractional-order systems
• Online Access: https://doi.org/10.34768/amcs-2020-0048

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.