Skip to main content
SpringerLink
Log in

Dynamic output-feedback guaranteed cost control for linear systems with uniform input quantization

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

There have existed the researches on guaranteed cost control for systems with the dynamic or logarithmic quantizer; however, intensive studies not only on continuous-time output-feedback linear systems with uniform input quantization but also on guaranteed cost control for such systems have not been carried out thus far. This paper first solves the problem of guaranteeing the linear quadratic (LQ) cost for continuous-time output-feedback linear systems with uniform input quantization. The proposed output-feedback controller comprises the main and the additional control parts. The former part is designed as a linear dynamic output-feedback controller for determining the fundamental characteristics of the system associated with the LQ cost, and the latter part is constructed as an integer multiple of the quantization level for eliminating the effect of uniform input quantization. The additional control part adopts the state estimate instead of the state itself, which causes the state estimation errors. By computing their quantity added to the upper bound of the LQ cost, this paper shows that the proposed controller still guarantees the LQ cost despite the state estimation errors.

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. Kalman, R.E.: Nonlinear aspects of sampled-data control systems. In: Proc. Symp. Nonlinear Circuit Theory, Brooklyn, NY (1956)

  2. Curry, R.E.: Estimation and control with quantized measurements. MIT Press, Cambridge (1970)

    MATH  Google Scholar 

  3. Brockett, R.W., Liberzon, D.: Quantized feedback stabilization of linear systems. IEEE Trans. Automat. Control 45(7), 1279–1289 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Liberzon, D.: Hybrid feedback stabilization of systems with quantized signals. Automatica 39(9), 1543–1554 (2003)

    Article  MathSciNet  Google Scholar 

  5. Tian, E., Yue, D., Zhao, X.: Quantised control design for networked control systems. IET Control Theory Appl. 1(6), 1693–1699 (2007)

    Article  Google Scholar 

  6. Azuma, S., Sugie, T.: Optimal dynamic quantizers for discrete-valued input control. Automatica 44(2), 396–406 (2008)

    Article  MathSciNet  Google Scholar 

  7. Goodwin, G.C., Quevedo, D.E., Silva, E.I.: Architectures and coder design for networked control systems. Automatica 44(1), 248–257 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Che, W., Yang, G.: State feedback ℋ∞ control for quantized discrete-time systems. Asian J. Control 10(6), 718–723 (2008)

    Article  MathSciNet  Google Scholar 

  9. Fu, M., Xie, L.: Quantized feedback control for linear uncertain systems. Int. J. Robust Nonlinear Control (2009). doi:10.1002/rnc.1466

    MathSciNet  Google Scholar 

  10. Choi, Y.J., Yun, S.W., Park, P.: Asymptotic stabilisation of system with finite-level logarithmic quantiser. Electron. Lett. 44(19), 1117–1119 (2008)

    Article  Google Scholar 

  11. Delchamps, D.F.: Stabilizing a linear system with quantized state feedback. IEEE Trans. Automat. Control 35(8), 916–924 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Fu, M., Xie, L.: The sector bound approach to quantized feedback control. IEEE Trans. Automat. Control 50(11), 1698–1711 (2005)

    Article  MathSciNet  Google Scholar 

  14. Gao, H., Chen, T., Lam, J.: A new delay system approach to network-based control. Automatica 44(1), 39–52 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gao, H., Chen, T.: A new approach to quantized feedback control systems. Automatica 44(2), 534–542 (2008)

    Article  MathSciNet  Google Scholar 

  16. Park, P., Choi, Y.J., Yun, S.W.: Eliminating effect of input quantisation in linear systems. Electron. Lett. 44(7), 456–457 (2008)

    Article  Google Scholar 

  17. Wong, W.S., Brockett, R.W.: Systems with finite communication bandwidth constraints—II: Stabilization with limited information feedback. IEEE Trans. Automat. Control 44(5), 1049–1053 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Yue, D., Peng, C., Tang, G.Y.: Guaranteed cost control of linear systems over networks with state and input quantisations. IEE Proc. Control Theory Appl. 153(6), 658–664 (2006)

    Article  MathSciNet  Google Scholar 

  19. Yun, S.W., Choi, Y.J., Park, P.: ℋ2 control of continuous-time uncertain linear systems with input quantization and matched disturbances. Automatica 45(10), 2435–2439 (2009)

    Article  MATH  Google Scholar 

  20. Choi, H.H.: Variable structure output feedback control design for a class of uncertain dynamic systems. Automatica 38(2), 335–341 (2002)

    Article  MATH  Google Scholar 

  21. Park, P., Choi, D.J., Kong, S.G.: Output feedback variable structure control for linear systems with uncertainties and disturbances. Automatica 43(1), 72–79 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  22. Kwatny, H.G., Teolis, C., Mattice, M.: Variable structure control of systems with uncertain nonlinear friction. Automatica 38(7), 1251–1256 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  23. Huang, Y.J., Wang, Y.J.: Steady-state analysis for a class of sliding mode controlled systems using describing function method. Nonlinear Dyn. 30(3), 223–241 (2002)

    Article  MATH  Google Scholar 

  24. Boyd, S., El Ghaoui, L., Feron, E., Balakrishman, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)

    Google Scholar 

  25. Packard, A., Zhou, K., Pandey, P., Becker, G.: A collection of robust control problems leading to LMIs. In: IEEE Conf. Decis. Control Bright. Engl., pp. 1245–1250 (1991)

Download references

Author information

Authors and Affiliations

  1. Electrical and Computer Engineering Division & Information Technology Convergence Engineering Division, Pohang University of Science and Technology, Pohang, Gyungbuk, 790-784, South Korea

    Sung Wook Yun, Yun Jong Choi & PooGyeon Park

Authors
  1. Sung Wook Yun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun Jong Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. PooGyeon Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to PooGyeon Park.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yun, S.W., Choi, Y.J. & Park, P. Dynamic output-feedback guaranteed cost control for linear systems with uniform input quantization. Nonlinear Dyn 62, 95–104 (2010). https://doi.org/10.1007/s11071-010-9701-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-010-9701-y

Keywords

Search

Navigation