Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

H∞ Control of Networked Control Systems with Two Additive Time-varying Delays

시변 시간지연을 갖는 네트워크 제어 시스템의 H∞ 제어

  • 김재만 (연세대학교 전기전자공학과) ;
  • 박진배 (연세대학교 전기전자공학과)
  • Received : 2012.10.11
  • Accepted : 2013.01.11
  • Published : 2013.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents a stabilization method for NCS (Networked Control Systems) with two additive time-varying delays. Each time delay component between the plant and the controller has different characteristics depending on communication network, and has the upper and lower bounds. The time delay occurring from the controller to the plant has an effect on the time delay occurring from the plant to the controller, and the relationship between two delays is taken into account on the stability analysis. Based on the two additive delay components and the bound conditions, the appropriate Lyapunov-Krasovskii functional and the LMI (Linear Matrix Inequality) method derive the stability condition and the $H_{\infty}$ norm constraint for time-varying delayed NCS. Simulation results are finally given to demonstrate the effectiveness of the proposed method.

Keywords

References

  1. G. C. Walsh, H. Ye, and L. G. Bushnell, "Stability analysis of networked control systems," IEEE Trans. Control Syst. Tech., vol. 10, no. 3, pp. 438-446, May 2002. https://doi.org/10.1109/87.998034
  2. S. Hirche, T. Matiakis, and M. Buss, "A distributed controller approach for delay-independent stability of networked control systems," Automatica, vol. 45, no. 8, pp. 1828-1836, Aug. 2009. https://doi.org/10.1016/j.automatica.2009.04.016
  3. W. Zhang and L. Yu, "A robust control approach to stabilization of networked control systems with time-varying delays," Automatica, vol. 45, no. 10, pp. 2440-2445, Oct. 2009. https://doi.org/10.1016/j.automatica.2009.05.024
  4. G. P. Liu, Y. Xia, D. Rees, and W. Hu, "Design and stability criteria of networked predictive control systems with random network delay in the feedback channel," IEEE Trans. Syst. Man Cybern., vol. 37, no. 2, pp. 173-184, Mar. 2007. https://doi.org/10.1109/TSMCC.2006.886987
  5. G. S. Bae and Y. H. Joo, "Intelligent controller for networked control systems with time-delay," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 17, no. 2, pp. 139-144, Feb. 2011. https://doi.org/10.5302/J.ICROS.2011.17.2.139
  6. H. S. Han, "Stability bounds of time-varying uncertainty and delay time for discrete systems with time-varying delayed state", Journal of Institute of Control, Robotics and Systems (in Korean), vol. 18, no. 10, pp. 895-901, Oct. 2012. https://doi.org/10.5302/J.ICROS.2012.18.10.895
  7. X. Xue and D. Qiu, "Robust $H_{{\infty}}$ compensator design for time-delay systems with norm-bounded time-varying uncertainties," IEEE Trans. Automatic Control, vol. 45, no. 7, pp. 1363-1369, Jul. 2000. https://doi.org/10.1109/9.867049
  8. Y. S. Lee, Y. S. Moon, W. H. Kwon, and P. G. Park, "Delay-dependent robust $H_{{\infty}}$ control for uncertain systems with a state-delay," Automatica, vol. 40, no. 1, pp. 65-72, Jan. 2004. https://doi.org/10.1016/j.automatica.2003.07.004
  9. F. Yang, Z. Wang, D. W. C. Ho, and M. Gani, "Robust $H_{{\infty}}$ control with missing measurements and time delays," IEEE Trans. Automatic Control, vol. 52, no. 9, pp. 1666-1672, Sep. 2007. https://doi.org/10.1109/TAC.2007.904250
  10. H. Gao, T. Chen, and J. Lam, "A new delay system approach to network-based control," Automatica, vol. 44, no. 1, pp. 39-52, Jan. 2008. https://doi.org/10.1016/j.automatica.2007.04.020
  11. M. B. G. Cloosterman, N. V. D. Wouw, W. P. M. H. Heemels, and H. Nijmeijer, "Stability of networked control systems with uncertain time-varying delays," IEEE. Trans. Automatic Control, vol. 54, no. 7, pp. 1575-1580, Jul. 2009. https://doi.org/10.1109/TAC.2009.2015543
  12. W. A. Zhang and L. Yu, "New approach to stabilisation of networked control systems with time-varying delays," IET Control Theory and Applications, vol. 2, no. 12, pp. 1094-1104, Dec. 2008. https://doi.org/10.1049/iet-cta:20070291
  13. L. Dritsas and A. Tzes, "Robust stability bounds for networked controlled systems with unknown, bounded and varying delays," IET Control Theory and Applications, vol. 3, no. 3, pp. 270-280, Mar. 2009. https://doi.org/10.1049/iet-cta:20070384
  14. X. Jiang, Q.-L. Han, S. Liu, and A. Xue, "A new $H_{{\infty}}$ stabilization criterion for networked control systems," IEEE Trans. Automatic Control, vol. 53, no. 4, pp. 1025-1032, May 2008. https://doi.org/10.1109/TAC.2008.919547
  15. D. Huang and S. K. Nguang "Robust disturbance attenuation for uncertain networked control systems with random time delays," IET Control Theory and Applications, vol. 2, no. 11, pp. 1008-1023, Nov. 2008. https://doi.org/10.1049/iet-cta:20080037
  16. F. Yang, Z. Wang, Y. S. Hung, and M Gani, "$H_{{\infty}}$ control for networked systems with random communication delays," IEEE Trans. Automatic Control, vol. 51, no. 3, pp. 511-518, Mar. 2006. https://doi.org/10.1109/TAC.2005.864207
  17. E. Tian, D. Yue, and Y. Zhang, "On improved delay-dependent robust $H_{{\infty}}$ control for systems with interval time-varying delay," Journal of Frank. Institute, vol. 348, no. 4, pp. 555-567, May 2011. https://doi.org/10.1016/j.jfranklin.2011.01.001
  18. H. Zhang, M. Li, J. Yang, and D. Yang, "Fuzzy model- based robust networked control for a class of nonlinear systems," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 39, no. 2, pp. 437-446, Mar. 2009. https://doi.org/10.1109/TSMCA.2008.2010787
  19. R. Dey, G. Ray, S. Ghosh, and A. Rakshit, "Stability analysis for continuous system with additive time-varying delays: A less conservative result," Applied Math. and Comp., vol. 215, no. 10, pp. 3740-3745, Jan. 2010. https://doi.org/10.1016/j.amc.2009.11.014

Cited by

  1. Outdoor Localization for a Quad-rotor using Extended Kalman Filter and Path Planning vol.20, pp.11, 2014, https://doi.org/10.5302/J.ICROS.2014.14.0013