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Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer

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Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
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Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong district, Hanoi 100000, Vietnam
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Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group, 167 Hoang Ngan, Hanoi 100000, Vietnam
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Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, India
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Department ELEC, Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium
*
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in 8th International Conference on Modern Circuits and Systems Technologies (MOCAST), Thessaloniki, Greece, 13–15 May 2019.
Technologies 2019, 7(4), 76; https://doi.org/10.3390/technologies7040076
Received: 26 September 2019 / Revised: 20 October 2019 / Accepted: 22 October 2019 / Published: 24 October 2019
In this work a novel chaotic system with a line equilibrium is presented. First, a dynamical analysis on the system is performed, by computing its bifurcation diagram, continuation diagram, phase portraits and Lyapunov exponents. Then, the system is applied to the problem of secure communication. We assume that the transmitted signal is an additional state. For this reason, the nonlinear system is rewritten in a rectangular descriptor form and then an observer is constructed for achieving synchronization and input reconstruction. If we assume some rank conditions (on the nonlinearities and the solvability of a linear matrix inequality (LMI)) on the system matrices then the observer synchronization can be feasible. We evaluate and demonstrate our approach with specific numerical results. View Full-Text
Keywords: descriptor systems; chaos; synchronization; observer design; secure communication; hidden attractors; linear matrix inequality (LMI) descriptor systems; chaos; synchronization; observer design; secure communication; hidden attractors; linear matrix inequality (LMI)
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MDPI and ACS Style

Moysis, L.; Volos, C.; Pham, V.-T.; Goudos, S.; Stouboulos, I.; Gupta, M.K.; Mishra, V.K. Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer. Technologies 2019, 7, 76.

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