Title: A novel four-leaf chaotic system, its control and synchronisation via integral sliding mode control

Authors: Sundarapandian Vaidyanathan; Ahmed Rhif

Addresses: Research and Development Centre, Vel Tech University, Avadi-Vel Tech Road, Avadi, Chennai-600 062, Tamil Nadu, India ' Laboratory of Advanced Systems, Polytechnic School of Tunisia, BP 743, 2078 La Marsa, Tunisia

Abstract: This paper describes a novel 3D four-leaf chaotic system and details its qualitative properties. The novel chaotic system is a polynomial system with three quadratic nonlinearities. The phase portraits of the novel four-leaf chaotic system are illustrated. We show that the novel chaotic system has three unstable equilibrium points. The Lyapunov exponents of the novel chaotic system are calculated as L₁ = 1.0299, L₂ = 0 and L₃ = −7.0268. The Lyapunov dimension of the novel chaotic system is found as D_L = 2.1466. Next, we apply integral sliding mode control method to find a feedback control law that globally stabilises the novel four-leaf chaotic system. Furthermore, we apply integral sliding mode control method to find a feedback control law that globally synchronises two identical four-leaf chaotic systems. The global control and synchronisation results are proved using Lyapunov stability theory. MATLAB simulations are shown to illustrate all the sliding mode control results derived in this work.

Keywords: chaos; chaotic systems; four-leaf system; sliding control; integral sliding mode control; global chaos synchronisation.

DOI: 10.1504/IJMIC.2017.085295

International Journal of Modelling, Identification and Control, 2017 Vol.28 No.1, pp.28 - 39

Received: 29 Apr 2016
Accepted: 13 Jun 2016
Published online: 21 Jul 2017 *

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