Control of Shimizu–Morioka Chaotic System with Passive Control, Sliding Mode Control and Backstepping Design Methods: A Comparative Analysis

  • Uğur Erkin Kocamaz
  • Yilmaz Uyaroğlu
  • Sundarapandian Vaidyanathan
Part of the Studies in Computational Intelligence book series (SCI, volume 636)


This chapter investigates the control of continuous time Shimizu–Morioka chaotic system with unknown system parameters by means of three different control approaches, namely passive control, sliding mode control and backstepping design. Based on the properties of sliding mode control theory, the appropriate surfaces are designed. Lyapunov functions are used to realize that the passive controller and backstepping controllers ensure the global asymptotic stability of the system. Owing to the controllers, the Shimizu–Morioka chaotic system stabilizes towards its equilibrium points in the state space. Numerical simulations are performed to show and compare the efficiency of the proposed control methods.


Shimizu–Morioka chaotic system Passive control Sliding mode control Backstepping design Chaos control 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Uğur Erkin Kocamaz
    • 1
  • Yilmaz Uyaroğlu
    • 2
  • Sundarapandian Vaidyanathan
    • 3
  1. 1.SakaryaTurkey
  2. 2.Faculty of Engineering, Department of Electrical & Electronics EngineeringSakarya UniversitySakaryaTurkey
  3. 3.Research and Development CentreVel Tech Dr. RR and Dr. SR Technical UniversityAvadi, ChennaiIndia

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