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Title: Stability analysis and robust synchronisation of fractional-order modified Colpitts oscillators

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

Addresses: Laboratory of Condensed Matter-Electronics and Signal Processing (LAMACET), Faculty of Sciences, Department of Physics, University of Dschang, Cameroon ' Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh, KSA; Faculty of Computers and Artificial Intelligence, Benha University, Egypt ' Laboratoire de Matière Condensée d'Electronique et de Traitement du Signal, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon; Research Group on Experimental and Applied Physics for Sustainable Development (EAPhySuD), P.O. Box 412, Dschang, Cameroon ' Laboratory of Condensed Matter-Electronics and Signal Processing (LAMACET), Faculty of Sciences, Department of Physics, University of Dschang, Cameroon

Abstract: Based on the stability theory of the fractional order system, the dynamic behaviours of the uncertain Colpitts oscillator with fractional order-derivative is studied. Furthermore, based on the extended bounded real lemma, the robust controller is obtained using the drive-response synchronisation concept together with the Lyapunov stability theory formulated using the fractional Lyapunov direct method where the fractional-order q belongs to 0 < q < 1. In order to bring out the dynamic behaviour of this system, their phase portraits, the bifurcation diagrams and the Lyapunov exponent are simulated. Moreover, in this work, an approximated solution for both systems to show that the solution of such a system can be represented as a simple power-series function is provided. This study equally provides a systematic procedure to highlight the simplicity and flexibility of the suggested control approach. Simulations with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.

Keywords: Lyapunov exponent; bifurcation; chaos; fractional modified Colpitts oscillator; H? synchronisation; robust controller.

DOI: 10.1504/IJAAC.2020.103806

International Journal of Automation and Control, 2020 Vol.14 No.1, pp.52 - 79

Received: 16 Jan 2018
Accepted: 17 Apr 2018

Published online: 12 Nov 2019 *

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