Skip to main content
SpringerLink
Log in

Lyapunov’s Stability Theory

  • Reference work entry
  • First Online:
Encyclopedia of Systems and Control

  • 140 Accesses

Abstract

Lyapunov’s theory for characterizing and studying the stability of equilibrium points is presented for time-invariant and time-varying systems modeled by ordinary differential equations.

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 1,699.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
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

Bibliography

  • Bacciotti A, Rosier L (2005) Liapunov functions and stability in control theory, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  • Haddad WM, Chellaboina V (2008) Nonlinear dynamical systems and control. Princeton University Press, Princeton

    Book  MATH  Google Scholar 

  • Hahn W (1967) Stability of motion. Springer, New York

    Book  MATH  Google Scholar 

  • Khalil HK (2002) Nonlinear systems, 3rd edn. Prentice Hall, Princeton

    MATH  Google Scholar 

  • Krasovskii NN (1963) Stability of motion. Stanford University Press, Stanford

    MATH  Google Scholar 

  • Michel AN, Wang K (1995) Qualitative theory of dynamical systems. Marcel Dekker, New York

    Google Scholar 

  • Qu Z (1998) Robust control of nonlinear uncertain systems. Wiley-Interscience, New York

    MATH  Google Scholar 

  • Rouche N, Habets P, Laloy M (1977) Stability theory by Lyapunov’s direct method. Springer, New York

    Book  MATH  Google Scholar 

  • Sastry S (1999) Nonlinear systems: analysis, stability, and control. Springer, New York

    Book  MATH  Google Scholar 

  • Slotine J-JE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Vidyasagar M (2002) Nonlinear systems analysis, classic edn. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Yoshizawa T (1966) Stability theory by Liapunov’s second method. The Mathematical Society of Japan, Tokyo

    MATH  Google Scholar 

  • Zubov VI (1964) Methods of A. M. Lyapunov and their applications. P. Noordhoff Ltd., Groningen

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA

    Hassan K. Khalil

Authors
  1. Hassan K. Khalil
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Technological Leadership Institute, University of Minnesota, Minneapolis, MA, USA

    Tariq Samad

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Khalil, H.K. (2021). Lyapunov’s Stability Theory. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_77

Download citation

Publish with us

Policies and ethics

Search

Navigation