Composite nonlinear feedback control technique for master/slave synchronization of nonlinear systems

Abstract

In this paper, we propose a design approach of composite nonlinear feedback control technique for the synchronization of master/slave nonlinear systems with time-varying delays, Lipschitz nonlinear functions and parametric uncertainties. Based on the Lyapunov–Krasovskii stabilization theory and linear matrix inequalities, a new sufficient condition is generated for the synchronization of chaotic systems with nonlinearities and perturbations on the master and slave systems. By using the Barbalat’s lemma, the proposed control method guarantees that the states of the master and slave systems are synchronized with an asymptotic convergence rate. Simulation results are demonstrated on two forms of Chua’s chaotic system, which illustrate that the suggested design technique yields satisfactory transient performance.

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Acknowledgments

This research project was supported by a grant from the “Research Center of the Center for Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University.

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Correspondence to Saleh Mobayen.

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Mobayen, S., Tchier, F. Composite nonlinear feedback control technique for master/slave synchronization of nonlinear systems. Nonlinear Dyn 87, 1731–1747 (2017). https://doi.org/10.1007/s11071-016-3148-8

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Keywords

  • Synchronization
  • Composite nonlinear feedback
  • Linear matrix inequalities
  • Master/slave systems
  • Performance improvement