Skip to main content
SpringerLink
Log in

On Stability of Linear Systems with Impulsive Action at the Matrix

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We discuss properties of stability and asymptotic stability of solutions to linear systems of differential equations with generalized actions in matrices of systems. We obtain sufficient conditions that guarantee the stability and asymptotic stability of solutions to these system. A distinctive feature of systems considered is the fact that the right-hand sides of systems contain the ill-posed operation of multiplication of discontinuous functions by generalized functions.

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. D. L. Andrianov, V. O. Arbuzov, S. V. Ivliev, V. P. Maksimov, and P. M. Simonov, “Dynamical models of Economics: Theory, applications, and software,” Vestn. Perm. Univ. Ser. Ekon., 27, No. 4, 8–32 (2015).

    Google Scholar 

  2. V. A. Dykhta and O. N. Samsonyuk, Optimal Impulsive Control and Applications [in Russian], Fizmatlit, Moscow (2003).

    MATH  Google Scholar 

  3. I. A. Kornilov and A. N. Sesekin, “On stability of linear systems with matrix containing generalized functions,” Vestn. UGTU-UPI, 33, No. 3, 386–388 (2004).

    Google Scholar 

  4. V. P. Maksimov, “Positional parring of impulsive perturbances in a control problem for linear systems with aftereffect,” Vestn. Perm. Univ. Ser. Ekon., 21, No. 2, 6–14 (2014).

    Google Scholar 

  5. B. M. Miller and V. Ya. Rubinovich, “Discontinuous solutions to optimal control problems and their representation by singular space-time transforms,” Avtomat. Telemekh., No. 12, 56–103 (2013).

  6. A. M. Samoilenko and N. A. Perestyuk, Differential Equations with Impulsive Actions pin Russian], Vyshcha Shkola, Kiev (1987).

  7. A. N. Sesekin, “Dynamical systems with nonlinear impulsive structure,” Tr. Inst. Mat. Mekh. Ural Otd. Ross. Akad. Nauk, 6, No. 2, 497–514 (2000).

    Google Scholar 

  8. A. N. Sesekin and N. I. Zhelonkina, “On the stability of linear systems with generalized action and delay,” Proc. 18th IFAC World Congr., IFAC-PapersOnLine, 13404–13407, Milano, Italy (2011).

  9. S. T. Zavalishchin and A. N. Sesekin, Dynamic Impulse Systems: Theory and Applications, Kluwer, Dordrecht (1997).

  10. N. I. Zhelonkina, A. N. Sesekin, and S. P. Sorokin, “On stability of linear systems with impulsive action at the matrix of system and delay,” Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 1, 40–46 (2011).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. N. N. Krasovsky Institute of Mathematics and Mechanics of the Ural Branch of the RAS, Yekaterinburg, Russia

    N. I. Zhelonkina & A. N. Sesekin

  2. Ural Federal University named after the first President of Russia B. N. Yeltsin, Yekaterinburg, Russia

    A. N. Sesekin

Authors
  1. N. I. Zhelonkina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Sesekin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. I. Zhelonkina.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhelonkina, N.I., Sesekin, A.N. On Stability of Linear Systems with Impulsive Action at the Matrix. J Math Sci 230, 673–676 (2018). https://doi.org/10.1007/s10958-018-3767-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-018-3767-3

Keywords and phrases

AMS Subject Classification

Search

Navigation