<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>z</italic>-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.</p></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.

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

Faculty of Electronics, Telecommunications and Informatics

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new...

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

Published Online: Dec 31, 2020

Page range: 649 - 658

Received: Jan 21, 2020

Accepted: Jun 07, 2020

DOI: https://doi.org/10.34768/amcs-2020-0048

Keywords
stability analysis, discrete-time systems, fractional-order systems

© 2020 Łukasz Grzymkowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Dec 31, 2020

Page range: 649 - 658

Received: Jan 21, 2020

Accepted: Jun 07, 2020

DOI: https://doi.org/10.34768/amcs-2020-0048

Keywordsstability analysis, discrete-time systems, fractional-order systems

© 2020 Łukasz Grzymkowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
stability analysis, discrete-time systems, fractional-order systems