Skip to main content

Advertisement

SpringerLink
Log in

Constructing exponential estimates in compartmental systems with distributed delays: an approach based on the hale–lunel inequality

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

This paper presents a method for constructing exponential estimates in a compartmental system with distributed delays on the basis of the Hale–Lunel inequality and its application. The practical importance of this study is illustrated by a pharmacokinetic model from anesthesiology.

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. V. I. Rozhkov, “An estimate for solutions of a difference equation,” Trans. of the Seminar on the Theory of Differential Equations with a Divergent Argument, No. 9, 39–52 (1975).

  2. D. Ya. Khusainov, “Estimates for solutions of linear functional-differential equations of neutral type,” Ukr. Mat. Zh., No. 9, 1123–1135 (1991).

  3. V. Kertesz, “Stability investigations and exponential estimations for functional differential equations of retarded type,” Acta Mathematica Hungarica, 55, Nos. 3–4, 365–378 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Ya. Khusainov and V. P. Martsenyuk, “Double-ended estimates for solutions of linear systems with delay,” Dop. NAN Ukr., No. 8, 8–13 (1996).

  5. T. Wang, “Exponential stability and inequalities of solutions of abstract functional differential equations,” J. Math. Analysis and Appl., 324, No. 2, 982–991 (2006).

    Article  MATH  Google Scholar 

  6. W. M. Haddad and V. Chellaboina, “Stability theory for nonnegative and compartmental dynamical systems with time delay,” Systems and Control Letters, 51, No. 5, 335–361 (2004).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. I. Ya. Horbachevsky Ternopil State Medical University, Ternopil, Ukraine

    V. P. Martsenyuk & N. M. Gandzyuk

  2. Lutsk National Technical University, Lutsk, Ukraine

    I. Ye. Andrushchak

Authors
  1. V. P. Martsenyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Ye. Andrushchak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. M. Gandzyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Martsenyuk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 26–31, May–June 2013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martsenyuk, V.P., Andrushchak, I.Y. & Gandzyuk, N.M. Constructing exponential estimates in compartmental systems with distributed delays: an approach based on the hale–lunel inequality. Cybern Syst Anal 49, 347–352 (2013). https://doi.org/10.1007/s10559-013-9517-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-013-9517-0

Keywords

Search

Navigation