Skip to main content
SpringerLink
Log in

Stabilization Via Optimization

  • Chapter
New Trends in Systems Theory

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 7))

  • 439 Accesses

Abstract

We study the problem of existence, and construction, of a continuous asymptotically stabilizing feedback control (ASFC) x → u(x) which makes the zero solution of the n-dimensional, real analytic, affine system

$$\dot{x} = {{X}_{0}}(x) + u{{X}_{1}}(x), {{X}_{0}}(0) = 0, {{X}_{1}}(0) \ne 0$$
((1))

locally asymptotically stable.

This research was supported by NSF grant DMS-8721917.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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.

References

  1. H. Hermes, “Homogeneous Coordinates and Continuous Asymptotically Stabilizing Feedback Controls”, (to appear) Differential Equations, Stability and Control (Ed., S. Elaydi), Marcel Dekker (1990).

    Google Scholar 

  2. R. M. Bianchini and G. Stefani, “Graded Approximations and Controllability along a Trajectory”, (to appear) SIAM J. Control, and Opt.

    Google Scholar 

  3. L. P. Rothschild and E. M. Stein, “Hypoelliptic Differential Operators and Nilpotent Groups”, Acta Math. 137 (1976), 247–320.

    Article  Google Scholar 

  4. R. W. Brockett, “Asymptotic Stability and Feedback Stabilization”, Diff. Geometric Control Theory ,Brockett-Millman-Sussmann Eds., Birkhauser, Boston, 27 (1983), 181–191.

    Google Scholar 

  5. J. M. Coron, “A Necessary Condition for Feedback Stabilization”, (to appear) System and Control Letters (1990).

    Google Scholar 

  6. M. Kawski, “Stabilization of Nonlinear Systems in the Plane”, Systems and Control Letters 12 (1989), 169–175.

    Article  Google Scholar 

  7. H. J. Sussmann, A General Theorem on Local Controllability, SIAM J. Control and Opt. 25 (1987), 158–194.

    Article  Google Scholar 

  8. H. Hermes and M. Kawski, “Local Controllability of a Single-Input Affine System”, Nonlinear Anal, and Appl ,Lecture Notes in Pure and Appl. Math #100, Lakshmikantham, Ed., Marcel Dekker, Inc., NY (1987), 235–248.

    Google Scholar 

  9. H. Hermes, “Asymptotically Stabilizing Feedback Controls and the Nonlinear Regulator Problem”, (to appear) SIAM J. Control and Opt.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Box 426, Boulder, CO, 80309-0426, USA

    Henry Hermes

Authors
  1. Henry Hermes
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Hermes, H. (1991). Stabilization Via Optimization. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_47

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0439-8_47

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6760-7

  • Online ISBN: 978-1-4612-0439-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation