Skip to main content
SpringerLink
Log in

On right-hand uniqueness of solutions to nondegenerated algebro-differential equations with discontinuances

  • Determinate Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A finite-dimensional nondegenerate system of algebro-differential equations with discontinuances is considered. An equivalent system of discontinuous differential equations is constructed. Conditions of right-hand uniqueness of solution and of convergence of numerical methods are given.

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. Penleve, P., Lektsii o trenii (Lections on Friction), Moscow: Gostekhizdat, 1954.

    Google Scholar 

  2. Boyarintsev, Yu.E., Lineinye i nelineinye algebro-differentsial’nye sistemy (Linear and Nonlinear Algebro-Differential Systems), Novosibirsk: Nauka, 2000.

    Google Scholar 

  3. Filippov, A.F., Differentsial’nye uravneniya s razryvnoi pravoi chast’yu (Differential Equations with Discontinuous Right-hand Side), Moscow: Nauka, 1985.

    Google Scholar 

  4. Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya (Sliding Modes in Control Optimization), Moscow: Nauka, 1981.

    Google Scholar 

  5. Matrosov, V.M., On Differential Equations and Inequalities with Discontinuous Right-hand Sides. I, II, Diff. Uravn., 1967, vol. 3, no. 3, pp. 395–409; no. 5, pp. 839–848.

    MathSciNet  Google Scholar 

  6. Aizerman, M.A. and Pyatnitski, E.S., Fundamentals of the Theory of Discontinuous Systems. I, II, Avtom. Telemekh., 1974, nos. 7, 11.

  7. Bakhvalov, N.S., Zhidkov, N.P., and Kobel’kov, G.M., Chislennye metody (Numerical Methods), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  8. Filippov, A.F., Uniqueness of the Solution of a System of Differential Equations Unsolved for the Derivatives, Vestn. Mosk. Gos. Univ., 2004.

  9. Tikhonov, A.N., Differential Equation Systems That Contain Small Parameters with Derivatives, Mat. Sb., 1952, vol. 1(73), pp. 575–586.

    Google Scholar 

  10. Vasil’eva, A.B. and Butuzov, V.F., Asimptoticheskie razlozheniya reshenii singulyarno-vozmushchennykh uravnenii (Asymptotic Expansions of Solutions to Singularly Disturbed Equations), Moscow: Nauka, 1973.

    Google Scholar 

  11. Matrosov, I.V., Existence of Solutions of the Algebro-Differential Equations, Avtom. Telemekh., 2006, no. 9, pp. 61–69.

Download references

Author information

Authors and Affiliations

  1. Center of Stability and Nonlinear Dynamics Studies, Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow, Russia

    I. V. Matrosov

Authors
  1. I. V. Matrosov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © I.V. Matrosov, 2007, published in Avtomatika i Telemekhanika, 2007, No. 1, pp. 11–19.

This work was supported by Program no. 18 “Dynamics and Stability of the Multicomponent Machine Systems with Regard for Man-caused Safety” of the Department of Power Engineering, Machine Building, Mechanics, and Control Processes, Russian Academy of Sciences.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Matrosov, I.V. On right-hand uniqueness of solutions to nondegenerated algebro-differential equations with discontinuances. Autom Remote Control 68, 9–17 (2007). https://doi.org/10.1134/S000511790701002X

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000511790701002X

PACS numbers

Search

Navigation