Title: Fractional inverse full state hybrid projective synchronisation

Authors: Adel Ouannas; Ahmad Taher Azar; Toufik Ziar

Addresses: Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa, 12002, Algeria ' Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh, Saudi Arabia; Faculty of Computers and Artificial Intelligence, Benha University, Egypt ' Department of Material Sciences, University of Tebessa, 12002, Algeria

Abstract: Referring to fractional-order systems, this paper investigates the inverse full state hybrid projective synchronisation (IFSHPS) of non-identical systems characterised by different dimensions and different orders. By taking a master system of dimension n and a slave system of dimension m, the method enables each master system state to be synchronised with a linear combination of slave system states, where the scaling factor of the linear combination can be any arbitrary real constants. Based on fractional Lyapunov approach and stability theory of linear fractional-order systems, the method enables commensurate and incommensurate fractional-order systems with different dimension to be synchronised. Two different numerical examples are reported. The examples clearly highlight the capability of the conceived approach in effectively achieving synchronised dynamics for any scaling constants.

Keywords: full state hybrid projective synchronisation; fractional chaos; incommensurate and commensurate systems; fractional Lyapunov approach.

DOI: 10.1504/IJAIP.2020.109511

International Journal of Advanced Intelligence Paradigms, 2020 Vol.17 No.3/4, pp.279 - 298

Received: 19 Apr 2017
Accepted: 18 Jun 2017

Published online: 11 Sep 2020 *

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