Stability and applications of multi-order fractional systems | Zendy

Javier A. Gallegos | Zendy

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Stability and applications of multi-order fractional systems

Author(s) -

Javier A. Gallegos

Publication year - 2021

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2021274

Subject(s) - lipschitz continuity , stability (learning theory) , order (exchange) , mathematics , nonlinear system , exponential stability , class (philosophy) , population , control theory (sociology) , pure mathematics , computer science , control (management) , physics , finance , quantum mechanics , machine learning , artificial intelligence , sociology , economics , demography

This paper establishes conditions for global/local robust asymptotic stability for a class of multi-order nonlinear fractional systems consisting of a linear part plus a global/local Lipschitz nonlinear term. The derivation order can be different in each coordinate and take values in \begin{document}$ (0, 2) $\end{document} . As a consequence, a linearized stability theorem for multi-order systems is also obtained. The stability conditions are order-dependent, reducing the conservatism of order-independent ones. Detailed examples in robust control and population dynamics show the applicability of our results. Simulations are attached, showing the distinctive features that justify multi-order modelling.

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