International Journal of Control, Automation, and Systems

  • 제4권4호
  • /
  • Pages.516-523
  • /
  • 2006
  • /
  • 1598-6446(pISSN)
  • /
  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

[ $H_{\infty}$ ] Control of 2-D Discrete State Delay Systems

  • Xu Jianming (College of Information Engineering, Zhejiang University of Technology) ;
  • Yu Li (College of Information Engineering, Zhejiang University of Technology)
  • 발행 : 2006.08.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper is concerned with the $H_{\infty}$ control problem of 2-D discrete state delay systems described by the Roesser model. The condition for the system to have a specified $H_{\infty}$ performance is derived via the linear matrix inequality (LMI) approach. Furthermore, a design procedure for $H_{\infty}$ state feedback controllers is given by solving a certain LMI. The design problem of optimal $H_{\infty}$ controllers is formulated as a convex optimization problem, which can be solved by existing convex optimization techniques. Simulation results are presented to illustrate the effectiveness of the proposed results.

키워드

참고문헌

  1. T. Kaczorek, Two-dimensional Linear Systems, Lecture Notes in Control and Information Sciences, vol. 68, Springer-Verlag, Berlin, 1985
  2. R. N. Bracewell, Two-dimensional Imaging, Prentice-Hall Signal Processing Series, Prentice-Hall, Englewood Cliffs, NJ, 1995
  3. W. S. Lu and A. Antoniou, Two-dimensional Digital Filters, Electrical Engineering and Electronics, vol. 80, Marcel Dekker, New York, 1992
  4. D. D. Givone and R. P. Roesser, 'Multidimensional linear iterative circuits general properties,' IEEE Trans. on Computers, vol. 21, no. 10, pp. 1067-1073, 1972 https://doi.org/10.1109/T-C.1972.223453
  5. R. P. Roesser, 'A discrete state-space model for linear image processing,' IEEE Trans. on Automatic Control, vol. 20, no. 1, pp. 1-10, 1975 https://doi.org/10.1109/TAC.1975.1100844
  6. E. Fornasini and G. Marchesini, 'State-space realization theory of two-dimensional filters,' IEEE Trans. on Automatic Control, vol. 21, no. 4, pp. 484-491, 1976 https://doi.org/10.1109/TAC.1976.1101305
  7. J. E. Kurek, 'The general state-space model for a two-dimensional linear digital system,' IEEE Trans. on Automatic Control, vol. 30, no. 6, pp. 600-602, 1985 https://doi.org/10.1109/TAC.1985.1103998
  8. C. Du and L. Xie, 'LMI approach to output feedback stabilization of 2-D discrete systems,' International Journal of Control, vol. 72, no. 2, pp. 97-106, 1999 https://doi.org/10.1080/002071799221262
  9. J. C. Doyle, K. Glover, P. P. Khargoneker, and B. A. Francis, 'State-space solutions to standard $H_{2}$ and $H_{\infty}$ control problem,' IEEE Trans. on Automatic Control, vol. 34, no. 5, pp. 831-847, 1989 https://doi.org/10.1109/9.29425
  10. P. Gahinet and P. Apkarian, 'A linear matrix inequality approach to $H_{\infty}$ control,' International Journal of Robust and Nonlinear Control, vol. 4, no. 4, pp. 421-448, 1994 https://doi.org/10.1002/rnc.4590040403
  11. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, Englewood Cliffs, NJ, 1996
  12. M. Sebek, '$H_{\infty}$ problem of 2-D systems,' Proc. of European Control Conference, pp. 1476-1479, 1993
  13. C. Du and L. Xie, $H_{\infty}$ Control and Filtering of Two-dimensional Systems, Springer-Verlag, Berlin, 2002
  14. S. I. Niculescu, Delay Effects on Stability: A Rrobust Control Approach, Springer-Verlag, London, 2001
  15. L. Yu and J. Chu, 'An LMI approach to guaranteed cost control of linear uncertain timedelay systems,' Automatica, vol. 35, no. 6, pp. 1155-1159, 1999 https://doi.org/10.1016/S0005-1098(99)00007-2
  16. E. Fridman and U. Shaked, 'Delay-dependent stability and $H_{\infty}$ control: Constant and timevarying delays,' International Journal of Control, vol. 76, no. 1, pp. 48-60, 2003 https://doi.org/10.1080/0020717021000049151
  17. M. S. Mahmoud and A. Ismail, 'New results on delay-dependent control of time-delay systems,' IEEE Trans. on Automatic Control, vol. 50, no. 1, pp. 95-100, 2005 https://doi.org/10.1109/TAC.2004.841130
  18. W. Paszke, J. Lam, K. Galkowski, S. Xu, and Z. Lin, 'Robust stability and stabilization of 2D discrete state-delayed systems,' Systems & Control Letters, vol. 51, no. 3-4, pp. 277-291, 2004 https://doi.org/10.1016/j.sysconle.2003.09.003