Robust Chaos Synchronization for Chua’s Circuits via Active Sliding Mode Control

  • Olfa Boubaker
  • Rachid Dhifaoui
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


In this paper, we construct, in presence of model uncertainties and external disturbances, a robust active sliding controller to achieve master slave synchronization for Chua’s circuits. The master circuit is considered as a nominal system whereas parameter uncertainties affect the slave system. Using a Lyapunov approach and a reaching condition in the sliding surface, it will be shown that finite time synchronization can be guaranteed under an explicit relation between control parameters and the level of uncertainties. Numerical simulations are presented to estimate robustness of the proposed approach.


Slide Mode Controller Slave System Chaos Synchronization Synchronization Problem Robust Synchronization 
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  1. Agiza HN, Yassen M (2001) Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys Lett Sect A Gen At Solid State Phys 278(1):191–197MathSciNetzbMATHGoogle Scholar
  2. Bai EW, Lonngren KE (1997) Synchronization of two Lorenz systems using active control. Chaos Solit Fract 8(1):51–58ADSCrossRefzbMATHGoogle Scholar
  3. Banerjee S, Roy Chowdhury A (2009) Lyapunov function, parameter estimation, synchronization and chaotic cryptography. Commun Nonlin Sci Numer Simul 14(5):2248–2254CrossRefzbMATHGoogle Scholar
  4. Banerjee S, Rondoni L, Mitra M (2011) Applications of chaos and nonlinear dynamics in science and engineering, vol 1. Springer, BerlinCrossRefGoogle Scholar
  5. Banerjee S, Mitra M, Rondoni L (2012) Applications of chaos and nonlinear dynamics in science and engineering. Springer, BerlinCrossRefGoogle Scholar
  6. Banerjee S, Mitra M, Rondoni L (2013) Applications of chaos and nonlinear dynamics in science and engineering, vol 2. Springer, BerlinCrossRefGoogle Scholar
  7. Boubaker O (2008) Gain scheduling control: an LMI approach. Int Rev Electr Eng 3:378–385Google Scholar
  8. Boubaker O (2009) Master–slave synchronization for PWA systems. In: Proceedings of the 3rd IEEE international conference on signals, circuits and systems, pp 1–6Google Scholar
  9. Boubaker O, Babary JP (2003) On SISO and MIMO variable structure control of non linear distributed parameter systems: application to fixed bed reactors. J Process Control 13(8):729–737CrossRefGoogle Scholar
  10. Boubaker O, Babary JP, Ksouri M (2001) MIMO sliding mode control of a distributed parameter denitrifying biofilter. Appl Math Modell 25(8):671–682CrossRefzbMATHGoogle Scholar
  11. Cai N, Jing Y, Zhang S (2010) Modified projective synchronization of chaotic systems with disturbances via active sliding mode control. Commun Nonlin Sci Numer Simul 15(6):1613–1620MathSciNetCrossRefzbMATHGoogle Scholar
  12. Chua LO, Komuro M, Matsumoto T (1986) The double scroll family: I and II. IEEE Trans Circuit Syst 33(11):1072–1118MathSciNetADSCrossRefzbMATHGoogle Scholar
  13. Chua LO, Wu CW, Huang A, Zhong G (1993) A universal circuit for studying and generating chaos – part I: routes to chaos. IEEE Trans Circuit Syst 40(10):732–744MathSciNetADSCrossRefzbMATHGoogle Scholar
  14. Chua LO, Yang T, Zhong GQ, Wu CW (1996) Adaptive synchronization of Chua’s oscillators. Int J Bifurc Chaos Appl Sci Eng 6(1):189–201CrossRefGoogle Scholar
  15. Haeri M, Khademian B (2006) Comparison between different synchronization methods of identical chaotic systems. Chaos Solit Fract 29(4):1002–1022MathSciNetADSCrossRefzbMATHGoogle Scholar
  16. Ho MC, Hung YC (2002) Synchronization of two different systems by using generalized active control. Phys Lett Sect A Gen Atom Solid State Phys 301(5–6):424–428MathSciNetzbMATHGoogle Scholar
  17. Kennedy MP (1993) Three steps to chaos. Part II: a Chua’s circuit primer. IEEE Trans Circuit Syst I Fundam Theory Appl 40:657–674CrossRefzbMATHGoogle Scholar
  18. Luo ACJ (2009) A theory for synchronization of dynamical systems. Commun Nonlin Sci Numer Simul 14(5):1901–1951CrossRefzbMATHGoogle Scholar
  19. Mkaouar H, Boubaker O (2011) Sufficient conditions for global synchronization of continuous piecewise affine systems. Lect Notes Comput Sci 6752:199–211CrossRefGoogle Scholar
  20. Mkaouar H, Boubaker O (2012a) Chaos synchronization for master slave piecewise linear systems: application to Chua’s circuit. Commun Nonlin Sci Numer Simul 17(3):1292–1302MathSciNetCrossRefzbMATHGoogle Scholar
  21. Mkaouar H, Boubaker O (2012) On electronic design of the piecewise linear characteristic of the Chua’s diode: application to chaos synchronization. In: Proceedings of 16th IEEE Mediterranean electro-technical conference, pp 197–200Google Scholar
  22. Mkaouar H, Boubaker O (2013) On chaos synchronization of eminent examples of PWL systems via LMIs: a comparative study, submittedGoogle Scholar
  23. Tang F (2008) An adaptive synchronization strategy based on active control for demodulating message hidden in chaotic signals. Chaos Solit Frac 37(4):1090–1096ADSCrossRefGoogle Scholar
  24. Yang T, Chua LO (1997) Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans on Circuit Syst I Fundam Theory Appl 44(10):976–988MathSciNetCrossRefGoogle Scholar
  25. Zhang H, Ma XK, Liu WZ (2004) Synchronization of chaotic systems with parametric uncertainty using active sliding mode control. Chaos Solit Fract 21(5):1249–1257ADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.INSAT Centre Urbain NordNational Institute of Applied Sciences and TechnologyTunisTunisia

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