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Classification of Nonlinear Control Systems

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

Abstract

In this chapter, we study the classification of the affine nonlinear controlsystems of the form ( 1.10) repeated.

Keywords

Feedback Controller Output Feedback Lorenz System Inverse Dynamic Nonlinear Control System 
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.

References

  1. 1.
    Byrnes CI, Isidori A (1984) A frequency domain philosophy for nonlinear systems. In: Proceedings of the 23rd IEEE conference on decision and control, vol 23, pp 1569–1573Google Scholar
  2. 2.
    Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, New YorkCrossRefzbMATHGoogle Scholar
  3. 3.
    Huang J (2004) Nonlinear output regulation problem: theory and Applications. SIAM, PhiladelphiaCrossRefGoogle Scholar
  4. 4.
    Khalil H (2002) Nonlinear systems. Prentice Hall, Upper Saddle RiverzbMATHGoogle Scholar
  5. 5.
    Chen Z, Huang J (2002) Global robust stabilization of cascaded polynomial systems. Syst Control Lett 47:445–453CrossRefzbMATHGoogle Scholar
  6. 6.
    Chen Z, Huang J (2004) Dissipativity, stabilization, and regulation of cascade-connected systems. IEEE Trans Autom Control 49:635–650CrossRefGoogle Scholar
  7. 7.
    Ding Z (2003) Universal disturbance rejection for nonlinear systems in output feedback form. IEEE Trans Autom Control 48:1222–1226CrossRefGoogle Scholar
  8. 8.
    Huang J, Chen Z (2004) A general framework for tackling the output regulation problem. IEEE Trans Autom Control 49:2203–2218CrossRefGoogle Scholar
  9. 9.
    Jiang ZP, Mareels I (1997) A small-gain control method for nonlinear cascaded systems with dynamic uncertainties. IEEE Trans Autom Control 42:292–308CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Jiang ZP, Praly L (1993) Stabilization by output feedback for systems with ISS inverse dynamics. Syst Control Lett 21:19–33CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Khalil H (1994) Robust servomechanism output feedback controllers for feedback linearizable systems. Automatica 30:1587–1589CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Lin W, Gong Q (2003) A remark on partial-state feedback stabilization of cascade systems using small gain theorem. IEEE Trans Autom Control 48:497–500CrossRefMathSciNetGoogle Scholar
  13. 13.
    Serrani A, Isidori A, Marconi L (2001) Semiglobal nonlinear output regulation with adaptive internal model. IEEE Trans Autom Control 46:1178–1194CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Liu L, Huang J (2008) Asymptotic disturbance rejection of the Duffing’s system by adaptive output feedback control. IEEE Trans Circuits Syst II Express Briefs 55:1030–1066Google Scholar
  15. 15.
    Jiang ZP (2002) Advanced feedback control of the chaotic duffing equation. IEEE Trans Circuits Syst I Fundam Theory Appl 49:241–249Google Scholar
  16. 16.
    Nijmeijer H, Berghuis H (1995) On Lyapunov control of the Duffing equation. IEEE Trans Circuits Syst I Fundam Theory Appl 42:473–477CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Liang X, Zhang J, Xia X (2008) Adaptive synchronization for generalized Lorenz systems. IEEE Trans Autom Control 53:1740–1746CrossRefMathSciNetGoogle Scholar
  18. 18.
    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
  19. 19.
    Xu D, Huang J (2010) Robust adaptive control of a class of nonlinear systems and its applications. IEEE Trans Circuits Syst I Regul Pap 57:691–702CrossRefMathSciNetGoogle Scholar
  20. 20.
    Yu W (1999) Passive equivalence of chaos in Lorenz system. IEEE Trans Circuits Syst I Fundam Theory Appl 46:876–878CrossRefGoogle Scholar
  21. 21.
    Liao TL, Chen FW (1998) Control of Chua’s circuit with a cubic nonlinearity via nonlinear linearization technique. Circuits Syst Signal Process 17:719–731CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Liu L, Huang J (2006) Adaptive robust stabilization of output feedback systems with application to Chua’s circuit. IEEE Trans Circuits Syst II Express Briefs 53:926–930CrossRefGoogle Scholar
  23. 23.
    Zhong GQ (1994) Implementation of Chua’s circuit with a cubic nonlinearity. IEEE Trans Circuits Syst I Fundam Theory Appl 41:934–941CrossRefGoogle Scholar
  24. 24.
    Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Mathematical topics in population biology, morphogenesis and neurosciences. Springer, Berlin, pp 267–281Google 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

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