Open AccessStability and applications of multi-order fractional systems
Author(s) -
Javier A. Gallegos
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series 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.