Skip to main content

Part of the book series: Communications and Control Engineering ((CCE))

  • 920 Accesses

Abstract

One of the noticeable aspects of the theory of dynamics is the prevalence, since the work of Lyapunov and Poincaré, of first order differential equations. Of course, there are good conceptual and theoretical reasons for this, connected with the notion of state and the specification of initial conditions. Since the late fifties also areas as control theory have relented to this point of view. This introduction of state models in fact brought with it a renaissance in this field.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. J.C. Willems and H.L. Trentelman, On quadratic differential forms, SIAM Journal on Control and Optimization, to appear.

    Google Scholar 

  2. J.C. Willems, Paradigms and puzzles in the theory of dynamical systems, IEEE Transactions on Automatic Control, volume 36, pages 259–294, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. Cox, J. Little, and D. O’Shea, Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2nd edition, Springer Verlag, 1997.

    Google Scholar 

  4. M. Fliess, Automatique et corps différentiels, Forum Mathematicae, pages 227–238, 1989.

    Google Scholar 

  5. M. Fliess and S.T. Glad, An algebraic approach to linear and nonlinear control, pages 223–267 of Essays on Control: Perspectives in the Theory and Its Applications, edited by H.L. Trentelman and J.C. Willems, Birkhäuser, 1993.

    Google Scholar 

  6. E.D. Sontag, Polynomial Response Maps, Springer-Verlag, 1979.

    Google Scholar 

  7. Y. Wang and E.D. Sontag, Algebraic differential equations and rational control systems, SIAM Journal on Control and Optimization, volume 30, pages 1126–1149, 1992.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag London Limited

About this chapter

Cite this chapter

Willems, J.C. (1999). Lyapunov theory for high order differential systems. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_50

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0807-8_50

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1207-5

  • Online ISBN: 978-1-4471-0807-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics