Skip to main content
SpringerLink
Log in

Stabilization of Interconnected Discrete Systems with Quantization and Overflow Nonlinearities

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we address the problem of decentralized feedback control design for a class of linear interconnected discrete-time systems subject to quantization and overflow nonlinearities and unknown-but-bounded couplings. A decentralized quantized state feedback controller is designed at the subsystem level to render the closed-loop system asymptotically stable. When the local output measurements are available, a decentralized output-feedback quantized controller is developed attain similar asymptotic stability and guaranteed performance of the closed-loop quantized system. Several special cases of interest are derived and simulation results are provided.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. J. Baillieul, Feedback designs in information-based control, in Proc. Stochastic Theory and Control Workshop (2001), pp. 35–57

    Google Scholar 

  2. L. Bakule, Decentralized control: an overview. Annu. Rev. Control 32, 87–98 (2008)

    Article  Google Scholar 

  3. T. Bose, Combined effects of overflow and quantization in fixed-point digital filters. Digit. Signal Process. 4(4), 239–244 (1994)

    Article  Google Scholar 

  4. R.W. Brockett, D. Liberzon, Quantized feedback stabilization of linear systems. IEEE Trans. Autom. Control 45, 1279–1289 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. D.F. Delchamps, Stabilizing a linear system with quantized state feedback. IEEE Trans. Autom. Control 35, 916–924 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  6. N. Elia, K. Mitter, Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46(9), 1384–1400 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. K.T. Erickson, A.N. Michel, Stability analysis of fixed-point digital filters using computer generated Lyapunov functions, part I: direct form and coupled form filters. IEEE Trans. Circuits Syst. 32(2), 113–132 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  8. E. Fridman, M. Dambrine, Control under quantization, saturation and delay: an LMI approach. Automatica 45(10), 2258–2263 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Fu, L. Xie, The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control 50, 1698–1711 (2005)

    Article  MathSciNet  Google Scholar 

  10. V.K.R. Kandanvli, H. Kar, An LMI condition for robust stability of discrete-time state-delayed systems using quantization/overflow nonlinearities. Signal Process. 89(11), 2092–2102 (2009)

    Article  MATH  Google Scholar 

  11. D. Liberzon, Hybrid feedback stabilization of systems with quantized signals. Automatica 39, 1543–1554 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. M.S. Mahmoud, Computer-Operated Systems Control (Marcel Dekker, New York, 1991)

    MATH  Google Scholar 

  13. M.S. Mahmoud, Decentralized Control and Filtering for Interconnected Dynamical Systems (CRC Press, New York, 2010)

    Book  Google Scholar 

  14. Y. Matsumoto, G. Zhai, Y. Mi, Stabilization of discrete-time LTI systems by hybrid quantized output feedback, in 46th Japan Joint Automatic Control Conference, Okayama (2003), pp. 799–802

    Google Scholar 

  15. D.D. Siljak, Decentralized Control of Complex Systems (Academic, Cambridge, 1991)

    Google Scholar 

  16. S.S. Stankovic, D.M. Stipanovic, D.D. Siljak, Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems. Automatica 43, 861–867 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Tatikonda, S. Mitter, Control under communication constraints. IEEE Trans. Autom. Control 49(7), 1056–1068 (2004)

    Article  MathSciNet  Google Scholar 

  18. H. Zhai, Y. Mi, J. Imae, T. Kobayashi, Design of \(\mathcal{H}_{\infty}\) feedback control systems with quantized signals, in 16th IFAC World Congress, Prague (2005). Paper code: Fr-M17-TO/1

    Google Scholar 

Download references

Acknowledgements

This research work is supported by the deanship of scientific research (DSR) at KFUPM through research project No. RG1105-1.

Author information

Authors and Affiliations

  1. Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran, 31261, Saudi Arabia

    Magdi S. Mahmoud

Authors
  1. Magdi S. Mahmoud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Magdi S. Mahmoud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahmoud, M.S. Stabilization of Interconnected Discrete Systems with Quantization and Overflow Nonlinearities. Circuits Syst Signal Process 32, 905–917 (2013). https://doi.org/10.1007/s00034-012-9480-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-012-9480-4

Keywords

Search

Navigation