• Zhiyong ChenEmail author
  • Jie Huang
Part of the Advanced Textbooks in Control and Signal Processing book series (C&SP)


Nonlinear systems are ubiquitous in the real world. In this chapter, we first introduce the state space description of nonlinear systems, nonlinear control systems, and nonlinear control laws in Sect. 1.1. Then, in Sect. 1.2, we describe three specific nonlinear control systems and use them to illustrate the stabilization problem and the output regulation problem of nonlinear systems. Finally, in Sect. 1.3, we close this chapter with the organization of this book.


Lorenz System Hubble Space Telescope Disturbance Rejection Nonlinear Control System Permanent Magnet Synchronous Motor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Baik IC, Kim KH, Youn MJ (2000) Robust nonlinear speed control of pm synchronous motor using boundary layer intergral sliding mode control technique. IEEE Trans Control Syst Technol 8:47–54CrossRefGoogle Scholar
  2. 2.
    Corron NJ (2010) A simple circuit implementation of a chaotic Lorenz system. Creative consulting for research and educationGoogle Scholar
  3. 3.
    Dixon WE, Behal A, Dawson DM, Nagarkatti SP (2003) Nonlinear control of engineering systems: a Lyapunov-based approach. Birkhäuser, BaselCrossRefGoogle Scholar
  4. 4.
    Foster CL, Tinker ML, Nurre GS, Till WA (1995) The solar array-induced disturbance of the hubble space telescope pointing system. NASA Technical Paper 3556Google Scholar
  5. 5.
    Klumpp AR (1976) Singularity free extraction of a quaternion from a direction cosine matrix. J Spacecraft Rockets 13:754–755CrossRefGoogle Scholar
  6. 6.
    Liang X, Zhang J, Xia X (2008) Adaptive synchronization for generalized Lorenz systems. IEEE Trans Autom Control 53:1740–1746CrossRefMathSciNetGoogle Scholar
  7. 7.
    Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141CrossRefGoogle Scholar
  8. 8.
    Ping Z, Huang J (2012) Speed tracking control of pm synchronous motor by internal model design. Int J Control 85:522–532CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Sidi MJ (1997) Spacecraft dynamics and control. Cambridge University Press, CambridgeGoogle Scholar
  10. 10.
    Simpson DG (2011) UTC and the hubble space telescope flight software. AAS 11–673Google Scholar
  11. 11.
    Xu D, Huang J (2010) Global output regulation for output feedback systems with an uncertain exosystem and its application. Int J Robust Nonlinear Control 20:1678–1691CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Xu D, Huang J (2010) Robust adaptive control of a class of nonlinear systems and its applications. IEEE Trans Circuits Syst II Express Briefs 57:691–702CrossRefMathSciNetGoogle Scholar
  13. 13.
    Yu W (1999) Passive equivalence of chaos in Lorenz system. IEEE Trans Circuits Syst-I Fundam Theory Appl 46:876–878CrossRefGoogle Scholar
  14. 14.
    Zhu G, Desaint LA, Akhrif O, Kaddouri A (2000) Speed tracking control of a permanent-magnet synchronous motor with state and load torque observer. IEEE Trans Industr Electron 47:346–355CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceUniversity of NewcastleCallaghanAustralia
  2. 2.Department of Mechanical and Automation EngineeringThe Chinese University of Hong KongShatinChina

Personalised recommendations