Skip to main content
SpringerLink
Log in

Attraction domains of systems with polynomial nonlinearities

  • Nonlinear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A novel method is presented for estimating attraction domains of the zero solution of systems of differential equations with stable linear component and nonlinear components of degrees two and three. A new class of Lyapunov functions is proposed. The efficiency of the approach is illustrated via examples.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brockett, R.W., Lie Algebras and Lie Groups in Control Theory, in Geometric Methods in System Theory. NATO Advanced Study Institutes Series, Mayne, D.Q. and Brockett, R.W., Eds., Dordrecht: D. Reidel, 1973, vol. 3, pp 43–82.

    Google Scholar 

  2. Barkin, A.I., Absolyutnaya ustoichivost’ sistem upravleniya (Absolute Stability of Control Systems), Moscow: URSS, 2012.

    Google Scholar 

  3. Barkin, A.I., Zelentsovskii, A.L., and Pakshin, P.V., Absolyutnaya ustoichivost’ determinirovannykh istokhasticheskikh sistem upravleniya (Absolute Stability of Deterministic and Stochastic Control Systems), Moscow: Mosk. Aviats. Inst., 1992.

    Google Scholar 

  4. Kamenetskii, V.A., Construction of Domains of Attraction by the Method of Lyapunov Functions, Autom. Remote Control, 1994, vol. 55, no. 6, part 1, pp. 778–791.

    Google Scholar 

  5. Chesi, G., Garulli, A., Tesi A., et al., LMI-based Computation of Optimal Quadratic Lypunov Functionsfor Odd Polynomial Systems, Int. J. Robust Nonlin. Control, 2005, vol. 15, no. 1, pp. 35–49.

    Article  Google Scholar 

  6. Valmorbida, G., Tarbouriech, S., and Garcia, G., Region of Attraction Estimates for Polynomial Systems, Proc. Joint 48th Conf. Decision Control and 28th Chinese Control Conf., Shanghai, 2009, pp. 5947–5952.

    Google Scholar 

  7. Vannelli, A. and Vidyasagar, M., Maximal Lyapunov Functions and Domains of Attraction for PolynomialDifferential Equations, Automatica, 1985, vol. 21, no. 1, pp. 69–80.

    Article  Google Scholar 

  8. Barkin, A.I., Computation of Attraction Domains for Systems with Polynomial Right-hand Side, Inform. Technol. Vychisl. Sist., 2013, no. 4, pp. 3–8.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    A. I. Barkin

Authors
  1. A. I. Barkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Barkin.

Additional information

Original Russian Text © A.I. Barkin, 2015, published in Avtomatika i Telemekhanika, 2015, No. 7, pp. 26–39.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barkin, A.I. Attraction domains of systems with polynomial nonlinearities. Autom Remote Control 76, 1156–1168 (2015). https://doi.org/10.1134/S0005117915070024

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117915070024

Keywords

Search

Navigation