Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Nonlinear Zero Dynamics

  • Alberto Isidori
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_83

Abstract

The notion of zero dynamics plays a role in nonlinear systems that is analogous to the role played, in a linear system, by the notion of zeros of the transfer function. In this article, we review the basic concepts underlying the definition of zero dynamics and discuss its relevance in the context of nonlinear feedback design.

Keywords

High-gain feedback Inverse systems Minimum-phase nonlinear systems Normal forms Output regulation Stabilization 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Byrnes CI, Isidori A (1984) A frequency domain philosophy for nonlinear systems. IEEE Conf Dec Control 23:1569–1573Google Scholar
  2. Byrnes CI, Isidori A (1991) Asymptotic stabilization of minimum-phase nonlinear systems. IEEE Trans Autom Control AC-36:1122–1137MathSciNetGoogle Scholar
  3. Byrnes CI, Isidori A, Willems JC (1991) Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear aystems. IEEE Trans Autom Control AC-36:1228–1240MathSciNetGoogle Scholar
  4. Francis BA, Wonham WM (1975) The internal model principle for linear multivariable regulators. J Appl Math Optim 2:170–194MathSciNetGoogle Scholar
  5. Freidovich LB, Khalil HK (2008) Performance recovery of feedback-linearization-based designs. IEEE Trans Autom Control 53:2324–2334MathSciNetGoogle Scholar
  6. Hirschorn RM (1979) Invertibility for multivariable nonlinear control systems. IEEE Trans Autom Control AC-24:855–865MathSciNetGoogle Scholar
  7. Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, Berlin/New YorkGoogle Scholar
  8. Isidori A, Byrnes CI (1990) Output regulation of nonlinear systems. IEEE Trans Autom Control AC-35:131–140MathSciNetGoogle Scholar
  9. Isidori A, Byrnes CI (2008) Steady-state behaviors in nonlinear systems, with an application to robust disturbance rejection. Ann Rev Control 32:1–16Google Scholar
  10. Isidori A, Moog C (1988) On the nonlinear equivalent of the notion of transmission zeros. In: CI Byrnes, A Kurzhanski (eds) Modelling and adaptive control. Lecture notes in control and information sciences, vol 105. Springer, Berlin/New York pp 445–471Google Scholar
  11. Isidori A, Krener AJ, Gori-Giorgi C, Monaco S (1981) Nonlinear decoupling via feedback: a differential geometric approach. IEEE Trans Autom Control AC-26:331–345MathSciNetGoogle Scholar
  12. Khalil HK, Esfandiari F (1993) Semiglobal stabilization of a class of nonlinear systems using output feedback. IEEE Trans Autom Control AC-38:1412–1415MathSciNetGoogle Scholar
  13. Liberzon D, Morse AS, Sontag ED (2002) Output-input stability and minimum-phase nonlinear systems. IEEE Trans Autom Control AC-43:422–436MathSciNetGoogle Scholar
  14. Seron MM, Braslavsky JH, Kokotovic PV, Mayne DQ (1999) Feedback limitations in nonlinear systems: from Bode integrals to cheap control. IEEE Trans Autom Control AC-44:829–833MathSciNetGoogle Scholar
  15. Singh SN (1981) A modified algorithm for invertibility in nonlinear systems. IEEE Trans Autom Control AC-26:595–598Google Scholar
  16. Silverman LM (1969) Inversion of multivariable linear systems. IEEE Trans Autom Control AC-14:270–276Google Scholar
  17. Sontag ED (1995) On the input–to–state stability property. Eur J Control 1:24–36Google Scholar
  18. Wonham WM (1979) Linear multivariable control: a geometric approach. Springer, New YorkGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Department of Computer and System Sciences “A. Ruberti”University of Rome “La Sapienza”RomeItaly