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A constructive approach for investigating the stability of incommensurate fractional differential systems

  • This paper is devoted to studying the asymptotic behaviour of solutions to generalized noncommensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary and sufficient to ensure the stability of such systems. Next, from the fractional-order pseudospectrum definition proposed by Sanca et al., we formulate the concept of a rational approximation for the fractional spectrum of a noncommensurate fractional systems with general, not necessarily rational, orders. Our first important new contribution is to show the equivalence between the fractional spectrum of a noncommensurate linear system and its rational approximation. With this result in hand, we use ideas developed in our earlier work to demonstrate the stability of an equilibrium point to nonlinear systems in arbitrary finite-dimensional spaces. A second novel aspect of our work is the fact that the approach is constructive. Finally, we give numerical simulations to illustrate the merit of the proposed theoretical results.

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Metadaten
Author:Kai Diethelm, Safoura Hashemishahraki, Ha Duc Thai, Hoang The Tuan
URN:urn:nbn:de:bvb:863-opus-51954
Document Type:Preprint
Language:English
Year of publication:2023
Publishing Institution:Technische Hochschule Würzburg-Schweinfurt
Release Date:2024/02/27
Pages/Size:21
Institutes and faculty:Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften
Licence (German):License LogoCreative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell - Weitergabe unter gleichen Bedingungen 4.0 International
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