Skip to main content
Log in

Consistency and eigenvalue assignment for discrete-time bilinear systems: I

  • Control Theory
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We introduce the notion of consistency for discrete-time linear control systems with incomplete feedback and bilinear systems. We obtain consistency criteria for time-varying systems. The property of consistency for time-independent systems is studied. The results obtained earlier for systems with continuous time are generalized to systems with discrete time.

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. Popova, S.N. and Tonkov, E.L., Control over the Lyapunov Exponents of Consistent Systems. I, Differ. Equ., 1994, vol. 30, no. 10, pp. 1556–1564.

    MathSciNet  MATH  Google Scholar 

  2. Zaitsev, V.A. and Tonkov, E.L., Attainability, Consistency and the Rotation Method by V.M. Millionshchikov, Russian Math., 1999, vol. 43, no. 2, pp. 42–52.

    MathSciNet  MATH  Google Scholar 

  3. Zaitsev, V.A., Consistent Systems and Pole Assignment: I, Differ. Equ., 2012, vol. 48, no. 1, pp. 120–135.

    Article  MathSciNet  MATH  Google Scholar 

  4. Zaitsev, V.A., Consistent Systems and Pole Assignment: II, Differ. Equ., 2012, vol. 48, no. 6, pp. 857–866.

    Article  MathSciNet  MATH  Google Scholar 

  5. Lancaster, P., Theory of Matrices, New York-London: Academic Press, 1969. Translated under the title Teoriya matrits, Moscow: Nauka, 1978.

    MATH  Google Scholar 

  6. Gaishun, I.V., Sistemy s diskretnym vremenem (Systems with Discrete Time), Minsk, 2001.

    MATH  Google Scholar 

  7. Kwakernaak, H. and Sivan, R., Linear Optimal Control Systems, New York-London-Sydney: Wiley-Interscience, 1972. Translated under the title Lineinye optimal’nye sistemy upravleniya, Moscow, 1977.

    MATH  Google Scholar 

  8. Popova, S.N. and Tonkov, E.L., Consistent Systems and Control of Lyapunov Exponents, Differ. Equ., 1997, vol. 33, no. 2, pp. 226–235.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Zaitsev.

Additional information

Original Russian Text © V.A. Zaitsev, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 11, pp. 1498–1509.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zaitsev, V.A. Consistency and eigenvalue assignment for discrete-time bilinear systems: I. Diff Equat 50, 1495–1507 (2014). https://doi.org/10.1134/S001226611411007X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S001226611411007X

Keywords

Navigation