Further Remarks on Irrational Systems and Their Applications †

Adrián-Josué Guel-Cortez, César-Fernando Méndez-Barrios, Diego Torres-García, Liliana Félix

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Irrational Systems (ISs) are transfer functions that include terms with irrational exponents. Since such systems are ubiquitous and can be seen when solving partial differential equations, fractional-order differential equations, or non-linear differential equations; their nature seems to be strongly linked with a low-order description of distributed parameter systems. This makes ISs an appealing option for model-reduction applications and controls. In this work, we review some of the fundamental concepts behind a set of ISs that are of core importance in their stability analysis and control design. Specifically, we introduce the notion of multivalued functions, branch points, time response, and stability regions, as well as some practical applications where these systems can be encountered. The theory is accompanied by some numerical examples or simulations.
Original languageEnglish
Article number5
Number of pages11
JournalComputer Sciences & Mathematics Forum
Issue number1
Publication statusE-pub ahead of print - 22 Dec 2022
Event5th Mexican Workshop on Fractional Calculus - Monterrey, Mexico
Duration: 5 Oct 20227 Oct 2022

Bibliographical note

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).


  • irrational systems
  • fractional-order control
  • model-reduction methods


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