Skip to main content
Springer Nature Link
Log in

A Lower Bound on Data Rates for Observability and Stabilizability of Linear Systems

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

This paper studies observability and stabilizability of linear time-invariant systems in the presence of limited feedback data rates. The well-known data-rate theorem in the literature presents a lower bound on data rates, above which there exists a quantization, coding, and control scheme such that an unstable dynamical system can be stabilized. However, it is unnecessary to transmit data packet on the plant state to the controller when the state prediction error is small enough. Thus, we reduce the conservatism of the prior results by employing a time-varying coding scheme. It is shown in our results that, there exists the lower bound on the data rate for observability and stabilizability, which is tighter than the ones in the data-rate theorem in the literature. Illustrative examples are given to demonstrate the effectiveness of the proposed quantization, coding, and control scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. Baillieul, J. and Antsaklis, P., Control and communication challenges in networked real time systems, Proceedings of IEEE Special Iss. Emerg. Technol. Netw. Control Syst, USA: IEEE, 2007, pp. 9–28.

  2. Minero, P., Franceschetti, M., Dey, S., and Nair, G.N., Data rate theorem for stabilization over time-varying feedback channels, IEEE Trans. Autom. Control, 2009, vol. 54, no. 2, pp. 243–255.

    Article  MathSciNet  MATH  Google Scholar 

  3. Baillieul, J., Feedback designs for controlling device arrays with communication channel bandwidth constraints, Proceedings of ARO Workshop on Smart Structures, Pennsylvania State Univ., 1999.

  4. Baillieul, J., Feedback designs in information based control, Proceedings of Stochastic Theory and Control Proceedings of a Workshop Held in Lawrence, Kansas, Pasik-Duncan, B., Ed., New York: Springer-Verlag, 2001, pp. 35–57.

  5. Baillieul, J., Data-rate requirements for nonlinear feedback control, Proceedings of 6th IFAC Symp. Nonlinear Control Syst., Stuttgart, 2004, pp. 1277–1282.

  6. Nair, G.N. and Evans, R.J., Stabilizability of stochastic linear systems with finite feedback data rates, SIAM J. Control Optim., 2004, vol. 43, no. 2, pp. 413–436.

    Article  MathSciNet  MATH  Google Scholar 

  7. Elia, N., When Bode meets Shannon: Control-oriented feedback communication schemes, IEEE Trans. Autom. Control, 2004, vol. 49, no. 9, pp. 1477–1488.

    Article  MathSciNet  MATH  Google Scholar 

  8. Tatikonda, S. and Mitter, S.K., Control under communication constraints, IEEE Trans. Autom. Control, 2004, vol. 49, no. 7, pp. 1056–1068.

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu, K., Fridman, E., and Hetel, L., Stability and L2-gain analysis of networked control systems under round-robin scheduling: A time-delay approach, Syst. Control Lett., 2006, vol. 61, no. 5, pp. 666–675.

    Article  MATH  Google Scholar 

  10. Sahebsara, M., Chen, T., and Shah, S.L., Optimal H∞ filtering in networked control systems with multiple packet dropouts, Syst. Control Lett., 2008, vol. 57, no. 9, pp. 696–702.

    Article  MathSciNet  MATH  Google Scholar 

  11. Gurt, A. and Nair, G.N., Internal stability of dynamic quantized control for stochastic linear plants, Automatica, 2009, vol. 45, no. 6, pp.1387–1396.

    Article  MATH  Google Scholar 

  12. Li, T. and Xie, L., Distributed coordination of multi-agent systems with quantized-observer based encoding-decoding, IEEE Trans. Autom. Control, 2012, vol. 57, no. 12, pp. 3023–3037.

    Article  MathSciNet  MATH  Google Scholar 

  13. Xue, B., Li, S., and Zhu, Q., Moving horizon state estimation for networked control systems with multiple packet dropouts, IEEE Trans. Autom. Control, 2012, vol. 57, no. 9, pp. 2360–2366.

    Article  MathSciNet  MATH  Google Scholar 

  14. Nair, G.N., A nonstochastic information theory for communication and state estimation, IEEE Trans. Autom. Control, 2013, vol. 58, no. 6, pp. 1497–1510.

    Article  MathSciNet  MATH  Google Scholar 

  15. Liu, Q. and Jin, F., State estimation for networked control systems using fixed data rates, Int. J. Syst. Sci., 2017, vol. 48, no. 9, pp. 1818–1828.

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu, Q., Minimum information rate for observability of linear systems with stochastic time delay, Int. J. Control, 2018.

  17. Yang, R., Liu, G., Shi, P., Thomas, C., and Basin, M.V., Predictive output feedback control for networked control systems, IEEE Trans. Ind. Electron., 2014, vol. 61, no. 1, pp. 512–520.

    Article  Google Scholar 

  18. Wu, L., Yang, R., Shi, P., and Su, X., Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings, Automatica, 2015, vol. 59, pp. 206–215.

    Article  MathSciNet  MATH  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

Author information

Authors and Affiliations

  1. College of Equipment Engineering, Shenyang Ligong University, Shenyang, China

    Qingquan Liu, Zheyuan Bi, Rui Ding & Fang Jin

Authors
  1. Qingquan Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zheyuan Bi
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Rui Ding
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Fang Jin
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Qingquan Liu.

Additional information

The article is published in the original.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qingquan Liu, Bi, Z., Ding, R. et al. A Lower Bound on Data Rates for Observability and Stabilizability of Linear Systems. Aut. Control Comp. Sci. 53, 80–89 (2019). https://doi.org/10.3103/S0146411619010097

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411619010097

Keywords: