Skip to main content
Log in

Robust stability of systems with delay

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider linear stationary systems of differential equations with delay. The matrices that determine the dynamics of a system vary within a certain interval. We obtain sufficient conditions for the robust stability of systems uniform with respect to delay and depending on the deviation of the argument.

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

Access this article

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

Instant access to the full article PDF.

References

  1. E. I. Jury, “Robustness of discrete systems. A survey,”Avtomat. Telemekh., No. 5, 3–28 (1990).

    Google Scholar 

  2. V. L. Kharitonov, “On the asymptotic stability of the equilibrium state for a family of systems of linear differential equations,”Differents. Uravn.,14, No. 11, 2086–2088 (1978).

    Google Scholar 

  3. V. L. Kharitonov, “On a generalization of the criterion of stability,”Izv. Akad. Nauk. Kaz. SSR,14, No. 11, 2086–2088 (1978).

    Google Scholar 

  4. Yu. M. Gusev, V. N. Efanov, V. G. Krymskii, and V. Yu. Rutkovskii, “Analysis and synthesis of linear interval dynamical systems (the state of the problem). Analysis of stability of interval matrices and synthesis of robust controllers,”Izv. Akad. Nauk SSSR. Tekh. Kibern., No. 2, 3–30 (1991).

    Google Scholar 

  5. J. Hale,Theory of Functional Differential Equations [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  6. D. Ya. Khusainov and A. N. Sharkovskii, “Stability of solutions of differential equations with delayed argument,” in:Functional and Differential-Difference Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1974), pp. 141–147.

    Google Scholar 

  7. D. Ya. Khusainov and E. A. Yun'kova, “Estimation of the magnitude of delay in linear differential systems with deviating argument,”Ukr. Mat. Zh.,35, No. 2, 261–264 (1983).

    Google Scholar 

  8. D. Ya. Khusainov, “Exponential estimation of solutions of linear systems with delay for arbitrary deviations of the argument,”Differents. Uravn.,25, No. 9, 1631–1633 (1989).

    Google Scholar 

  9. D. G. Korenevskii,Stability of Solutions of Deterministic and Stochastic Differential-Difference Equations [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  10. Te-Jen Su and Chuan-Guey Huang, “Robust stability of delay dependence for linear uncertain systems,”IEEE Trans., Automat. Contr.,37, No. 10, 1656–1659 (1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 859–863, June, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khusainov, D.Y., Mustafaeva, R. Robust stability of systems with delay. Ukr Math J 47, 989–994 (1995). https://doi.org/10.1007/BF01058788

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058788

Keywords

Navigation