Attractiveness and stability for Riemann-Liouville fractional systems

Gallegos, Javier A. and Duarte-Mermoud, Manuel A.: Attractiveness and stability for Riemann-Liouville fractional systems. Electronic journal of qualitative theory of differential equations 73. pp. 1-16. (2018)

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Abstract

We propose a novel approach to study the asymptotic behavior of solutions to Riemann–Liouville (RL) fractional equations. It is shown that the standard Lyapunov approach is not suited and an extension employing two (pseudo) state spaces is needed. Theorems of Lyapunov and LaSalle type for general multi-order (commensurate or non-commensurate) nonlinear RL systems are stated. It is shown that stability and passivity concepts are thus well defined and can be employed in L 2 -control. Main applications provide convergence conditions for linear time-varying and nonlinear RL systems having the latter a linear part plus a Lipschitz term. Finally, computational realizations of RL systems, as well as relationships with Caputo fractional systems, are proposed.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 73
Page Range: pp. 1-16
ISSN: 1417-3875
Uncontrolled Keywords: Differenciálegyenlet - frakcionált
Additional Information: Bibliogr.: p. 15-16. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 07. 12:14
Last Modified: 2018. Nov. 07. 12:14
URI: http://acta.bibl.u-szeged.hu/id/eprint/55743

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