Stability and applications of multi-order fractional systems

Javier Gallegos

doi:10.3934/dcdsb.2021274

Article Contents

2022, Volume 27, Issue 9: 5283-5296. Doi: 10.3934/dcdsb.2021274

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Stability and applications of multi-order fractional systems

Javier Gallegos

Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile

Received: September 2020

Revised: August 2021

Early access: November 2021

Published: September 2022

The author thanks the anonymous reviewers for their comments. This research was supported by CONICYTPCHA/National PhD scholarship program, 2018

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Abstract

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 $ (0, 2) $. 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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Mathematics Subject Classification: 34A08, 93D09.

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Figure 1. Robust performance

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Figure 2. Population dynamics depending on the derivation order

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