Skip to main content
SpringerLink
Log in

Stability of Differential-Algebraic Equations under Uncertainty

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider a linear time-invariant homogeneous system of first-order ordinary differential equations with a noninvertible matrix multiplying the derivative of the unknown vector function and with perturbed coefficients. We introduce a class of perturbations of the coefficient matrices of the system and determine conditions on the perturbations of this class under which they do not affect the internal structure of the system. We obtain sufficient conditions for the robust stability of the system under such perturbations.

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. Byers, R. and Nichols, N.K., On the stability radius of a generalized state-space system, Linear Algebra Appl., 1993, no. 188–189, pp. 113–134.

    Article  MathSciNet  MATH  Google Scholar 

  2. Du, N.H., Stability radii of differential-algebraic equations with structured perturbations, Syst. Control Lett., 2008, no. 57, pp. 546–553.

    Article  MATH  Google Scholar 

  3. Du, N.H., Thuan, D.D., and Liem, N.C., Stability radius of implicit dynamic equations with constant coefficients on time scales, Syst. Control Lett., 2011, no. 60, pp. 596–603.

    Article  MathSciNet  MATH  Google Scholar 

  4. Du, N.H. and Linh, V.H., Stability radii for linear time-varying differential-algebraic equations with respect to dynamics perturbations, J. Differ. Equations, 2006, no. 230, pp. 579–599.

    Article  MATH  Google Scholar 

  5. Chyan, C.J., Du. N.H., and Linh, V.H., On data-dependence of exponential stability and the stability radii for linear time-varying differential-algebraic systems, J. Differ. Equations, 2008, no. 245, pp. 2078–2102.

    Article  MATH  Google Scholar 

  6. Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988.

    MATH  Google Scholar 

  7. Shcheglova, A.A., Transformation of a linear differential-algebraic system to an equivalent form, in Tr. IX Mezhdunar. Chetaevskoi Konf. “Analiticheskaya mekhanika, ustoichivost’ i upravlenie dvizheniem” (Proc. IX Intern. Chetaev Conf. “Analitic Mechanics, Stability and Motion Control”), Irkutsk: Sib. Branch RAS, 2007, vol. 5, pp. 298–307.

    Google Scholar 

  8. Trenogin, V.A., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1980.

    Google Scholar 

  9. Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk, 664033, Russia

    A. A. Shcheglova & A. D. Kononov

Authors
  1. A. A. Shcheglova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. D. Kononov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Shcheglova.

Additional information

Original Russian Text © A.A. Shcheglova, A.D. Kononov, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 7, pp. 881–890.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shcheglova, A.A., Kononov, A.D. Stability of Differential-Algebraic Equations under Uncertainty. Diff Equat 54, 860–869 (2018). https://doi.org/10.1134/S0012266118070030

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266118070030

Search

Navigation