Skip to main content
SpringerLink
Log in

Invariance conditions for MIMO systems based on regularization

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

New constructive conditions for the invariance of linear MIMO systems are obtained by regularizing a symmetric matrix equation. The corresponding theorems underlying the analytical synthesis of an invariant system are presented.

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. G. V. Shchipanov, Avtom. Telemekh., No. 1, 49–66 (1939).

    Google Scholar 

  2. G. V. Shchipanov, Gyroscopic Instruments for Blind Flight (Obrgiz, Moscow, 1938) [in Russian].

    Google Scholar 

  3. G. V. Shchipanov and Invariance Theory (Works and Documents), Ed. by Z. M. Lezina and V. I. Lezin (Fizmatlit, Moscow, 2004) [in Russian].

  4. G. Basile and G. Marro, Sys. Control Lett. 9, 191–195 (1987).

    Article  MATH  Google Scholar 

  5. B. M. Chen, I. M. Y. Mareels, Y. Zheng, and C. Zhang, Automatica 36, 1717–1724 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Compta, J. Ferrer, and M. Peca, Linear Algebra Appl. 430, 1574–1589 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  7. W. M. Wonham, Linear Multivariable Control: A Geometric Approach (Springer-Verlag, New York, 1979; Nauka, Moscow, 1980).

    Google Scholar 

  8. M. Sh. Misrikhanov, Invariant Control of Multidimensional Systems: Algebraic Approach (Nauka, Moscow, 2007) [in Russian].

    Google Scholar 

  9. A. S. Morse, SIAM J. Control 11, 446–465 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  10. V. N. Bukov, S. V. Goryunov, and V. N. Ryabchenko, Autom. Remote Control 61 (11), 1759–1795 (2000).

    MATH  MathSciNet  Google Scholar 

  11. M. Sh. Misrikhanov and V. N. Ryabchenko, Dokl. Math. 84 (1), 591–593 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  12. N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, Dokl. Math. 91 (1), 64–67 (2015).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Korolev Rocket and Space Corporation “Energia,”, ul. Lenina 4a, Korolev, Moscow oblast, 141070, Russia

    N. E. Zubov & E. A. Mikrin

  2. Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

    M. Sh. Misrikhanov & V. N. Ryabchenko

Authors
  1. N. E. Zubov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Mikrin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Sh. Misrikhanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. N. Ryabchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. E. Zubov.

Additional information

Original Russian Text © N.E. Zubov, E.A. Mikrin, M.Sh. Misrikhanov, V.N. Ryabchenko, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 1, pp. 20–22.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zubov, N.E., Mikrin, E.A., Misrikhanov, M.S. et al. Invariance conditions for MIMO systems based on regularization. Dokl. Math. 92, 664–666 (2015). https://doi.org/10.1134/S106456241506006X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106456241506006X

Keywords

Search

Navigation