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

이산시간 지연 불확실 특이시스템의 지연 종속 및 변수 종속 강인 안정성

  • 김종해 (선문대학교 전자공학과)
  • Received : 2009.12.28
  • Accepted : 2010.02.16
  • Published : 2010.04.01

Abstract

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.

Keywords

References

  1. 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. https://doi.org/10.1360/aas-007-0714
  2. 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. https://doi.org/10.3724/SP.J.1004.2009.01101
  3. 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.
  4. 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. https://doi.org/10.1016/j.cam.2007.01.044
  5. 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. https://doi.org/10.1016/S0167-6911(99)00119-X
  6. 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. https://doi.org/10.1080/0020717021000023834
  7. 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. https://doi.org/10.1109/TAC.2004.828317
  8. 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. https://doi.org/10.1016/j.cam.2006.07.027
  9. 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. https://doi.org/10.1016/j.automatica.2008.09.005
  10. 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. https://doi.org/10.1109/TCSII.2006.884116
  11. 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. https://doi.org/10.1016/j.sysconle.2003.08.002
  12. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA; SIAM, 1994.