$H_\infty$ Controller Design for Discrete-time Linear Systems with Time-varying Delays in States using S-procedure

S-procedure를 이용한 상태에 시변 시간지연을 가지는 이산 선형 시스템에 대한 $H_\infty$ 제어기 설계

  • Kim, Ki-Tae (School of Electronic and Electrical Engineering, Kyungpook National University) ;
  • Cho, Sang-Hyun (School of Electronic and Electrical Engineering, Kyungpook National University) ;
  • Park, Hong-Bae (School of Electronic and Electrical Engineering, Kyungpook National University)
  • Published : 2002.03.01

Abstract

This paper deals with the H$_{\infty}$ control problems for discrete-time linear systems with time-varying delays in states. The existence condition and the design method of the H$_{\infty}$ state feedback controller are given. In this paper, the H$_{\infty}$ control law is assumed to be a memoryless state feedback, and the upper-bound of time-varying delay and S-procedure are used. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

References

  1. J. Hennet and S. Tarbouriech, 'Stability and stabilization of delay differential systems,' Automatica, vol. 33, pp. 347-354, 1997 https://doi.org/10.1016/S0005-1098(96)00185-9
  2. E. T. Jeung, D. C. Oh, J. H. Kim, and H. B. Park, 'Robust controller design for uncertain systems with time delays : LMI approach,' Automatica, vol. 32, pp. 1229-1231, 1996 https://doi.org/10.1016/0005-1098(96)00055-6
  3. J. H. Lee, S. W. Kim, and W. H. Kwon, 'Memoryless $H_{\infty}$ controllers for state delayed systems,' IEEE Trans. on Automat. Contr., vol. 39, pp. 159-162, 1994 https://doi.org/10.1109/9.273356
  4. X. Li and C. E. Souza, 'Criteria for robust stability and stabilization of uncertain linear systems with time-delay,' Automatica, vol. 33, pp. 1657-1662, 1997 https://doi.org/10.1016/S0005-1098(97)00082-4
  5. S. H. Song and J. K. Kim, '$H_{\infty}$ control of discrete-time linear systems with normbounded uncertainties and time delay in state,' Automatica, vol. 34, pp. 137-139, 1998 https://doi.org/10.1016/S0005-1098(97)00182-9
  6. S. H. Song, J. K. Kim, C. H. Yim, and H. C. Kim, '$H_{\infty}$ control of discrete-time linear systems with time-varying delays in state,' Automatica, vol. 35, pp. 1587-1591, 1999 https://doi.org/10.1016/S0005-1098(99)00057-6
  7. K. T. Kim, S. H. Cho, and H. B. Park, '$H_{\infty}$ control for discrete-time linear systems with time-varying delays in state,' in Proc. of IECON '01, pp. 707-711, Denver, Colorado, Nov. 2001 https://doi.org/10.1109/IECON.2001.976701
  8. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994
  9. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Math Works Inc., 1995