이산시간 지연 불확실 특이시스템의 지연 종속 및 변수 종속 강인 안정성

Delay-dependent and Parameter-dependent Robust Stability for Discrete-time Delayed Uncertain Singular Systems

  • 김종해 (선문대학교 전자공학과)
  • 투고 : 2009.12.28
  • 심사 : 2010.02.16
  • 발행 : 2010.04.01


The problem of delay-dependent and parameter-dependent robust stability condition for discrete-time uncertain singular systems with polytopic uncertainty and interval time-varying delay is considered. A new robust stability condition based on parameter-dependent Lyapunov function is derived in terms of LMI (linear matrix inequality). Moreover, the proposed robust stability condition is a general condition for both singular and non-singular systems. A numerical example is presented to demonstrate the effectiveness of the proposed method.


연구 과제 주관 기관 : 선문대학교


  1. S. Ma, C. Zhang, and Z. Cheng, "Delay-dependent robust $H_{\infty}$ control for uncertain discrete-time singular systems with time-delays," Journal of Computational and Applied Mathematics, vol. 217, pp. 194-211, 2008.
  2. Y. Xia and Y. Jia, "Robust stability functionals of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functions," International Journal of Control, vol. 75, pp. 1427-1434, 2002.
  3. H. Gao, P. Shi, and J. Wang, "Parameter-dependent robust stability of uncertain time-delay systems," Journal of Computational and Applied Mathematics, vol. 206, pp. 366-373, 2007.
  4. D. Peaucelle, D. Arzelier, J. Bachelier, and J. Bernussou, "A new robust D-stbility condition for real convex polytopic uncertainty," Systems & Control Letters, vol. 40, pp. 21-30, 2000.
  5. Y. He, M. Wu, J. H. She, and G. P. Liu, "Parameter-dependent Lyapunov functional for stability of time-delay systems of polytopic-type uncertainties," IEEE Trans. on Automatic Control., vol. 49, pp. 828-832, 2004.
  6. S. Xu and T. Chen, "Robust $H_{\infty}$ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers," Systems & Control Letters, vol. 51, pp. 171-183, 2004.
  7. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA; SIAM, 1994.
  8. X. M. Zhang and Q. L. Han, "Delay-dependent robust $H_{\infty}$ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality," IEEE Trans. Circuits and Systems-II, vol. 53, pp. 1466-1470, 2006.
  9. Z. Wu, H. Su, and J. Chu, "Improved results on delay-dependent $H_{\infty}$ control for singular time-delay systems," Acta Automatica Sinica, vol. 35, pp. 1101-1106, 2009.
  10. Z. Wu and W. Zhou, "Delay-dependent robust stabilization for uncertain singular systems with state delay," Acta Automatica Sinica, vol. 33, pp. 714-718, 2007.
  11. R. X. Zhong and Z. Yang, "Delay-dependent robust control of descriptor systems with time delay," Asian Journal of Control., vol. 8, pp. 36-44, 2006.
  12. J. Zhang, Y. Xia, and P. Shi, "Parameter-dependent robust $H_{\infty}$ filtering for uncertain discrete-time systems," Automatica, vol. 45, pp. 560-565, 2009.