Design of $H_{\infty}$ Control of Time-Delayed Linear Systems Using Model Transformation

모델변환을 이용한 시간지연 선형시스템의 지연종속 $H_{\infty}$ 제어

  • 마삼선 (한전 전력연구원 발전연구실) ;
  • 이희송 (충북대 공대 전기학과) ;
  • 김진훈 (충북대 공대 계측제어공학과)
  • Published : 2001.09.01

Abstract

This paper deals with the design of delay-dependent $H_{\infty}$ control for time-delayed linear systems. We propose the two different model transformations to handle efficiently the time delay and derive conditions linear matrix inequalities (LMI's) of which are dependent on the size of time-delay and its time-derivative. The $H_{\infty}$ controller is obtained by checking the feasibility of these LMI's. Finally, we show the usefulness and applicability of our results by an example.

Keywords

References

  1. M. M. Zavarei and M. Jamshidi, 'Time-Delay Systems Analysis, Optimization and Applications', North-Holland, 1987
  2. T. Mori and H. Konami, 'Stability of x(t)=Ax(t)+Bx(t-${\tau}$)', IEEE Trans. Auto. Contr., vol.34, pp. 460-462, 1989 https://doi.org/10.1109/9.28025
  3. J. H. Kim, 'Robust stability of linear systems with delayed perturbations,' IEEE Trans. Auto. Contr., vol.41, pp. 1820-1822, 1996 https://doi.org/10.1109/9.545749
  4. J. H. Su, 'Further results on the robust stability of linear systems with a single time delay,' Syst. Contr. Lett., vol.23, pp. 375-379, 1994 https://doi.org/10.1016/0167-6911(94)90071-X
  5. L. Xie and C. E. Souza, 'Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach', IEEE Trans. Auto. Contr. vol. 40, pp. 1144-1148, 1997 https://doi.org/10.1109/9.618244
  6. S. I. Niculescu, 'A Model Transformation Class for Delay-dependent Stability Analysis', Proceedings of the American Control Conference, San Diego, California Jun, pp. 314-318, 1999 https://doi.org/10.1109/ACC.1999.782791
  7. L. Xie and C. E. Souza, 'Delay-dependent robust $H_{\infty}$ control of uncertain linear state-delayed systems, Automatica, vol. 35, pp. 1313-1321, 1999 https://doi.org/10.1016/S0005-1098(99)00025-4
  8. L. Xie and C. E. Souza, 'Robust $H_{\infty}$ control for linear systems with norm-bouned time-varying uncertainly', IEEE Trans. Auto. Contr., vol. 37, pp. 1188-1191, 1992 https://doi.org/10.1109/9.151101
  9. Vladimir L. Kharitonov, Daniel Melchor-Aguilar, 'On delay-dependent stability conditions', Syst. Contr. Lett., vol. 40, pp.71-76, 2000 https://doi.org/10.1016/S0167-6911(00)00003-7