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Appendix

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

Abstract

In this section, we summarize some well known results on nonlinear systems without proof. These theorems are cited in Chaps.  2,  3 and  7, respectively.

Keywords

Nonlinear System System Theory Equilibrium Point Class Function Local Solution 
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.
    Jiang ZP, Teel AR, Praly L (1994) Small-gain theorem for ISS systems and applications. Math Control Signals Syst 7:95–120CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Lin Y (1992) Lyapunov function techniques for stabilization. Ph.D. thesis, Rutgers UniversityGoogle Scholar
  3. 3.
    Lin Y, Sontag ED, Wang Y (1993) Recent results on lyapunov theoretic techniques for nonlinear stability. In: Proceedings of the 1994 American control conference. Report SYCON-93-09Google Scholar
  4. 4.
    Isidori A (1999) Nonlinear control systems. Springer, New YorkzbMATHGoogle Scholar
  5. 5.
    Khalil H (2002) Nonlinear systems. Prentice Hall, New JerseyzbMATHGoogle Scholar
  6. 6.
    Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, New YorkCrossRefzbMATHGoogle Scholar
  7. 7.
    Carr J (1981) Applications of the center manifold theory. Springer, USACrossRefGoogle Scholar
  8. 8.
    Praly L, Jiang ZP (1993) Stabilization by output feedback for systems with ISS inverse dynamics. Syst Control Lett 21:19–33CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Qian C (2001) A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans Autom Control 46:1061–1079CrossRefzbMATHGoogle Scholar
  10. 10.
    Chen Z, Huang J (2005) A simplified small gain theorem for time-varying nonlinear systems. IEEE Trans Autom Control 50:1904–1908CrossRefGoogle Scholar
  11. 11.
    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

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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