Skip to main content
SpringerLink
Log in

\({\mathcal {H}}_\infty \) control of continuous-time uncertain linear systems with quantized-input saturation and external disturbances

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

Abstract

This paper introduces an \({\mathcal {H}}_\infty \) state- feedback controller for uncertain linear systems with quantized-input saturation and external disturbances. The proposed controller comprises two parts: a linear control part to achieve an \({\mathcal {H}}_\infty \) performance against model uncertainties and the mismatched part of the disturbances and a nonlinear control part to eliminate the effect of input quantization and the matched part of the disturbances, which provides the better disturbance attenuation performance than a controller that deals with a unified disturbance regardless of the presence of matched and mismatched parts. Simulation results confirm the effectiveness of the proposed controller.

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

Similar content being viewed by others

References

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

    Book  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Cao, Y.-Y., Sun, Y.-X., Lam, J.: Delay-dependent robust \(\cal {H}_{\infty }\) control for uncertain systems with time-varying delays. IEE Proc. Control Theory Appl. 145, 338–344 (1998)

    Article  Google Scholar 

  4. Cao, Y.Y., Lin, Z., Shamash, Y.: Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation. Syst. Control Lett. 46, 137–151 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Che, W., Yang, G.: Quantized dynamic output feedback \(\cal {H}_\infty \) control for discrete-time systems with quantizer ranges consideration. Acta Autom. Sinica 34, 652–658 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Che, W., Yang, G.: State feedback \(\cal {H}_\infty \) control for quantized discrete-time systems. Asian J. Control 10, 718–723 (2008)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  8. Corradini, M.L., Orlando, G.: Robust quantized feedback stabilization of linear systems. Automatica 44, 2458–2462 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Curry, R.E.: Estimation and Control with Quantized Measurements. M.I.T. Press, Cambridge, MA (1970)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  14. Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Birkhäuser, Boston (2001)

    Book  Google Scholar 

  15. Ishii, H., Başar, T.: Remote control of LTI systems over networks with state quantization. Syst. Control Lett. 54, 15–31 (2005)

    Article  MATH  Google Scholar 

  16. Kalman, R.E.: Nonlinear aspects of sampled-data control systems. In: Proceedings of the Symposium on Nonlinear Circuit Theory, Brooklyn, NY (1956)

  17. Kofman, E.: Quantized-state control. A method for discrete event control of continuous systems. Part II. In: Proceedings of RPIC’01, pp. 109–114, Santa Fe, Argentina (2001)

  18. Kofman, E.: Quantized-state control. A method for discrete event control of continuous systems. Part I. In: Proceedings of RPIC’01, pp. 103–108, Santa Fe, Argentina (2001)

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

    Article  MATH  MathSciNet  Google Scholar 

  20. Montestruque, L.A., Antsaklis, P.J.: Static and dynamic quantization in model-based networked control systems. Int. J. Control 80, 87–101 (2007)

    Article  MATH  MathSciNet  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, 72–79 (2007)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  23. Peng, C., Tian, Y.-C.: Networked \(\cal {H}_{\infty }\) control of linear systems with state quantization. Inf. Sci. 177, 5763–5774 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Song, G., Shen, H., Wei, Y., Li, Z.: Quantized output feedback control of uncertain discrete-time systems with input saturation. Circuits Syst. Signal Process 33, 3065–3083 (2014)

    Article  MathSciNet  Google Scholar 

  25. Techakittiroj, K., Loparo, K. A., Lin, W.: Stability of nonlinear continuous time systems with memoryless digital controllers. In: Proceedings of the American Control Conference, pp. 3985–3989, San Diego, California (1999)

  26. Wang, Y., Xie, L., de Souza, C.E.: Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19, 139–149 (1992)

    Article  Google Scholar 

  27. Wong, W.S., Brockett, R.W.: Systems with finite communication bandwidth constraints-II: stabilization with limited information feedback. IEEE Trans. Autom. Control 44, 1049–1053 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  28. 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, 658–664 (2006)

    Article  MathSciNet  Google Scholar 

  29. Yun, S.W., Choi, Y.J., Park, P.: \(\cal {H}_2\) control of continuous-time uncertain linear systems with input quantization and matched disturbances. Automatica 45, 2435–2439 (2009)

  30. 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)

    Article  MATH  MathSciNet  Google Scholar 

  31. Yun, S.W., Kim, S.H., Park, J.Y.: Asymptotic stabilization of continuous-time linear systems with input and state quantizations. Math. Probl. Eng. 2014, 1–6 (2014)

  32. Zheng, B., Yang, G.: Robust quantized feedback stabilization of linear systems based on sliding mode control. Optim. Control Appl. Methods 34, 458–471 (2013)

  33. Zheng, B., Yang, G.: Quantized output feedback stabilization of uncertain systems with input nonlinearities via sliding mode control. Int. J. Robust Nonlinear Control 24, 228–246 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  34. Zhou, J., Wen, C., Yang, G.: Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal. IEEE Trans. Autom. Control 39, 460–464 (2014)

    Article  MathSciNet  Google Scholar 

  35. Han, K., Chang, X.: Parameter-dependent robust H\(\infty \) filter design for uncertain discrete-time systems with quantized measurements. Int. J. Control, Autom. Syst. 11, 194–199 (2013)

Download references

Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2055122).

Author information

Authors and Affiliations

  1. Electrical Engineering Division, Pohang University of Science and Technology (POSTECH), Pohang, Gyungbuk, 790-784, Korea

    Bum Yong Park & PooGyeon Park

  2. Agency for Defense Development (ADD), Daejeon, Korea

    Sung Wook Yun

Authors
  1. Bum Yong Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sung Wook Yun
    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.

Additional information

B.Y. Park and S.W. Yun contributed equally to this work.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Park, B.Y., Yun, S.W. & Park, P. \({\mathcal {H}}_\infty \) control of continuous-time uncertain linear systems with quantized-input saturation and external disturbances. Nonlinear Dyn 79, 2457–2467 (2015). https://doi.org/10.1007/s11071-014-1825-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1825-z

Keywords

Search

Navigation