Variable Structure Control Design for Time-Delay Systems

시간 지연 시스템을 위한 가변 구조 제어기 설계

  • 최한호 (동국대학교 서울 전자전기공학부)
  • Received : 2010.02.16
  • Accepted : 2010.11.01
  • Published : 2010.12.01


We propose a variable structure control design method for a class of multivariable uncertain state-delayed systems which can be represented by polytopic models. In terms of LMIs, we derive a sufficient condition for the existence of a linear sliding surface guaranteeing the asymptotic stability of the sliding mode dynamics. We parameterize the sliding surface by using the solution of the LMI existence condition. We also give a switching feedback control strategy guaranteeing stable sliding mode. By using a numerical example, we show that our method supplements the existing results and it can be better than the existing results.


  1. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, “Linear matrix inequalities in system and control Theory,” Philadelphia, SIAM, 1994.
  2. E. M. Jafarov, “Robust sliding mode controllers design techniques for stabilization of multivariable time-delay systems with parameter perturbations and external disturbances,” Int. J. Systems Science, vol. 36, pp. 433-444, 2005.
  3. Y. Xia and Y. Jia, “Robust sliding-mode control for uncertain time-delay systems: An LMI approach,” IEEE Trans. on Automat. Contr., vol. 48, pp. 1086-1092, 2003.
  4. H.H. Choi, “Sliding-mode output feedback control design,” IEEE Trans. on Ind. Electron., vol. 55, pp. 4047-4054, 2008.
  5. R. El-Khazali, “Variable structure robust control of uncertain time-delay systems,” Automatica, vol. 34, pp. 327-332, 1998.
  6. S. Oucheriah, “Dynamic compensation of uncertain time-delay systems using variable structure approach,” IEEE Trans. on Circuits Syst. I, vol. 42, pp. 466-469, 1995.
  7. F. Gouaisbaut, M. Dambrine, and J. P. Richard, “Robust control of delay systems : A sliding mode control design via LMI,” Systems & Control Letters, vol. 46, pp. 219-230, 2002.
  8. S. H. Zak and S. Hui, “On variable structure output feedback controllers,” IEEE Trans. on Automat. Contr., vol. 38, pp. 1509-1512, 1993.

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