Skip to main content
SpringerLink
Log in

On stability of linear hybrid mechanical systems with distributed components

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We present a new approach to the solution of problems of stability of hybrid systems based on the constructive determination of elements of a matrix-valued functional.

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. A. V. Bartyshev, “Application of a vector Lyapunov function to the investigation of stability of two-component systems,” in: Vector Lyapunov Functions and Their Construction [in Russian], Nauka, Novosibirsk (1980), pp. 237–257.

    Google Scholar 

  2. V. A. Vujičić and A. A. Martynyuk, Some Problems of Mechanics of Nonautonomous Systems [in Russian], Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade (1991).

    Google Scholar 

  3. A. A. Martynyuk, “On practical stability of hybrid systems,” Prikl. Mekh., 25, No. 2, 101–107 (1989).

    MathSciNet  Google Scholar 

  4. O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  5. A. A. Martynyuk, “The Lyapunov matrix function and stability of hybrid systems,” Nonlin. Analysis, 10, No. 12, 1449–1457 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  6. V. I. Slyn’ko, “On conditions for the existence of solutions of one class of linear hybrid systems,” Dopov. Nats. Akad. Nauk Ukr., No. 5, 53–58 (2006).

  7. V. I. Slyn’ko, “On conditions for the existence of weak solutions of one class of linear hybrid systems,” Dopov. Nats. Akad. Nauk Ukr., No. 9, 56–62 (2006).

  8. A. A. Martynyuk, “On the theory of direct Lyapunov method,” Dokl. Akad. Nauk, 408, No. 3, 309–312 (2006).

    MathSciNet  Google Scholar 

  9. V. I. Slyn’ko, “Stability condition for linear impulsive systems with delay,” Int. Appl. Mech., 41, No. 6, 697–704 (2005).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine

    A. A. Martynyuk & V. I. Slyn’ko

Authors
  1. A. A. Martynyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Slyn’ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 204–216, February, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martynyuk, A.A., Slyn’ko, V.I. On stability of linear hybrid mechanical systems with distributed components. Ukr Math J 60, 235–252 (2008). https://doi.org/10.1007/s11253-008-0055-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0055-2

Keywords

Search

Navigation