Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 673–676 | Cite as

On Stability of Linear Systems with Impulsive Action at the Matrix

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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.

Keywords and phrases

differential equation impulsive action stability asymptotic stability 

AMS Subject Classification

34K45 

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References

  1. 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. 2.
    V. A. Dykhta and O. N. Samsonyuk, Optimal Impulsive Control and Applications [in Russian], Fizmatlit, Moscow (2003).MATHGoogle Scholar
  3. 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. 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. 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).Google Scholar
  6. 6.
    A. M. Samoilenko and N. A. Perestyuk, Differential Equations with Impulsive Actions pin Russian], Vyshcha Shkola, Kiev (1987).Google Scholar
  7. 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. 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).Google Scholar
  9. 9.
    S. T. Zavalishchin and A. N. Sesekin, Dynamic Impulse Systems: Theory and Applications, Kluwer, Dordrecht (1997).Google Scholar
  10. 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).CrossRefMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.N. N. Krasovsky Institute of Mathematics and Mechanics of the Ural Branch of the RASYekaterinburgRussia
  2. 2.Ural Federal University named after the first President of Russia B. N. YeltsinYekaterinburgRussia

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