Skip to main content
Log in

LMI-Based Criteria of Controllability and Observability for a Descriptor MIMO System

  • Control in Deterministic Systems
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

This paper develops simple LMI-based criteria of controllability and observability for a linear time-invariant descriptor (differential-algebraic) multiple-input multiple-output (MIMO) system. Several examples illustrate the efficiency of the developed criteria. A restriction of these criteria is that the number of inputs (outputs, respectively) must not be smaller than half the states of the space dimension.

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.

Similar content being viewed by others

References

  1. Handbook on the Theory of Automatic Control, Ed. by A. A. Krasovskii (Nauka, Moscow, 1987) [in Russian].

  2. Machine Building, Encyclopedy, Vol. 1–4: Automatic Control. The Theory (Mashinostroenie, Moscow, 2000) [in Russian].

  3. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems (Halsted, New York, 1977; Nauka, Moscow, 1977).

    MATH  Google Scholar 

  4. G. H. Golub and Ch. F. van Loan, Matrix Computations, Johns Hopkins Studies in Mathematical Sciences (Johns Hopkins Univ. Press, Baltimore, USA, 1996).

    Google Scholar 

  5. L. Dai, Singular Control Systems (Springer, Berlin, 1989).

    Book  MATH  Google Scholar 

  6. M. Sh. Misrikhanov and V. N. Ryabchenko, “Band criteria and recursive tests of complete controllability and observability of linear algebraic-differentiable systems,” Autom. Remote Control 69, 1486 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  7. N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Finite Eigenvalue assignment for a descriptor system,” Dokl. Math. 91, 64 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  8. N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Output control of the spectrum of a descriptor dynamical system,” Dokl. Math. 93, 259 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  9. N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “Spacecraft attitude control with simultaneous unloading of the angular momentum of inertial actuators,” J. Comput. Syst. Sci. Int. 54, 621 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  10. O. M. Budargin, M. Sh. Misrikhanov, and V. N. Ryabchenko, “The new criteria of large dynamic system controlability and observability,” Probl. Upravl., No. 1, 21–25 (2012).

    Google Scholar 

  11. J. W. Demmel, Applied Numerical Linear Algebra (SIAM, Philadelphia, 1997).

    Book  MATH  Google Scholar 

  12. M. Sh. Misrikhanov and V. N. Ryabchenko, “Algebraic and matrix methods in the theory of linear MIMO-systems,” Vest. IGEU, No. 5, 196–240 (2005).

    Google Scholar 

  13. R. E. Skelton, T. Iwasaki, and K. M. Grigoriadis, A Unified Algebraic Approach to Linear Control Design (Taylor and Francis, London, 1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. E. Zubov.

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. LMI-Based Criteria of Controllability and Observability for a Descriptor MIMO System. J. Comput. Syst. Sci. Int. 57, 18–24 (2018). https://doi.org/10.1134/S1064230718010148

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230718010148

Navigation