Title: Robust observer-based synchronisation of chaotic oscillators with structural perturbations and input nonlinearity

Authors: Kammogne Soup Tewa Alain; Ahmad Taher Azar; Fotsin Hilaire Bertrand; Kengne Romanic

Addresses: Laboratory of Electronics and Signal Processing, Department of Physic, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon ' College of Engineering, Prince Sultan University, Riyadh, KSA; Faculty of Computers and Artificial Intelligence, Benha University, Egypt ' Laboratory of Electronics and Signal Processing, Department of Physic, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon ' Laboratory of Electronics and Signal Processing, Department of Physic, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

Abstract: This paper presents a generalised robust adaptive chaotic synchronisation method for chaotic systems with structural perturbations. One control input is used to synchronise both systems exponentially fast based on Lyapunov theory. This approach cannot only make the outputs of both master and slave systems reach synchronisation with the passage of time between both systems but it can also reduce the effect of external perturbations and input nonlinearities. By assuming bounded solutions of the nominal uncoupled systems, sufficient conditions have been derived for boundedness of the solutions of two different classes of chaotic systems with input nonlinearity affected by structural perturbations. The propose approach offers a systematic design procedure for robust adaptive synchronisation of a large class of chaotic systems in the chaos research literature. As an illustration of the effectiveness and robustness of the proposed strategy, synchronisation problem of a master system consists of a perturbed modified Colpitts oscillator and an observer consisting of a Chua oscillator. It was found that the controller maintains robust stable synchronisation in the presence of exoteric perturbations and structural uncertainties.

Keywords: chaos synchronisation; adaptive observer; Lyapunov theory; H synchronisation; input nonlinearity.

DOI: 10.1504/IJAAC.2019.100467

International Journal of Automation and Control, 2019 Vol.13 No.4, pp.387 - 412

Received: 13 Sep 2017
Accepted: 30 Nov 2017

Published online: 29 Jun 2019 *

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