# 상태와 입력에 구간 시변 시간지연을 가지는 불확실 이산시간 특이시스템의 지연 종속 강인 $H_{\infty}$ 제어

• 김종해 (선문대학교 전자공학부)
• Published : 2009.01.01

#### Abstract

In this paper, we consider the design problem of delay-dependent robust $H{\infty}$ controller of discrete-time descriptor systems with parameter uncertainties and interval time-varying delays in state and control input by delay-dependent LMI (linear matrix inequality) technique. A new delay-dependent bounded real lemma for discrete-time descriptor systems with time-varying delays is derived. The condition for the existence of robust $H{\infty}$ controller and the robust $H{\infty}$ state feedback control law are proposed by LMI approach. A numerical example is demonstrated to show the validity of the design method.

#### References

1. S, Xu and C. Yang, '$\text H_\infty$ state feedback control for discrete singular systems,' IEEE Trans. on Automatic Control, vol. 45, no, 7, pp. 1405-1409, 2002 https://doi.org/10.1109/9.867074
2. G. Zhang and Y. Jia, 'New result on discrete-time bounded real lemma for singular systems: strict matrix inequality condition,' Proc. of American Control Conf, pp, 634-638, 2002
3. X. Ji, H. Su, and J Chu, 'Robust state feedback $\text H_\infty$ control for uncertain linear discrete singular systems,' lET Control Theory Appl., vol. 1, no, 1, pp. 195-200, 2007 https://doi.org/10.1049/iet-cta:20050482
4. S, Ma, C. Zhang, and Z, Cheng, 'Delay-dependent robust $\text H_\infty$ control for uncertain discrete-time singular systems with time delay,' Journal of Computational and Applied Mathematic, vol. 217, pp. 194-211, 2008 https://doi.org/10.1016/j.cam.2007.01.044
5. X. M. Zhang and Q. L. Han, 'Delay-dependent robust $\text H_\infty$ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality,' IEEE Trans. on Circuits and Systems, vol. 53, no. 12, pp. 1466-1470, 2006 https://doi.org/10.1109/TCSII.2006.884116
6. H. Wang, A. Xue, R. Lu, and Y. Chen, 'Delay-dependent robust $\text H_\infty$ control for uncertain discrete singular time-varying delay systems based on a finite sum inequality,' Proc. of the 26th Chinese Control Conf., pp. 595-599, 2007
7. I. R. Petersen, 'A stabilization algorithm for a class of uncertain linear systems,' Systems and Control Lett., vol. 31, pp. 129-138, 1987 https://doi.org/10.1016/0167-6911(87)90102-2
8. S. Xu and T. Chen, 'Robust $\text H_\infty$ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers,' Systems and Control Lett., vol. 51, pp. 171-183, 2004 https://doi.org/10.1016/j.sysconle.2003.08.002
9. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Math Works Inc., 1995