Delay-dependent Robust $H_{\infty}$ Filtering for Uncertain Descriptor Systems with Time-varying Delay

시변 시간지연을 가지는 불확실 특이시스템의 지연 종속 강인 $H_{\infty}$ 필터링

  • 김종해 (선문대학교 전자공학과)
  • Published : 2009.09.01

Abstract

This paper is concerned with the problem of delay-dependent robust $H_{\infty}$ filtering for uncertain descriptor systems with time-varying delay. The considering uncertainty is convex compact set of polytoic type. The purpose is the design of a linear filter such that the resulting filtering error descriptor system is regular, impulse-free, and asymptotically stable with $H_{\infty}$ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed descriptor systems is derived. Based on the derived BRL, a robust $H_{\infty}$ filter is designed in terms of linear matrix inequaltity (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.

Keywords

References

  1. A. Elsayed and M. J. Grimble, 'A new approach to H$_{\infty}$ design of optimal digital linear filters,' IMA J. Math. Control Inform, vol. 6, pp. 233-251, 1989 https://doi.org/10.1093/imamci/6.2.233
  2. C. E. de Souza, R. Palhares, and P. L. D. Peres, 'Robust H$_{\infty}$ filter design for uncertain linear systems with multiple time-varying state delays,' IEEE Trans. Signal Process., vol. 49, pp. 569-576, 2001 https://doi.org/10.1109/78.905882
  3. E. Fridman, U. Shaked, and L. Xie, 'Robust H$_{\infty}$ filtering of linear systems with time varying delay,' IEEE Trans. Signal Process., vol. 48, pp. 159-165, 2003 https://doi.org/10.1109/78.815486
  4. H. Gao and C. Wang, 'Delay-dependent robust H$_{\infty}$ and L$_{2}$-L$_{\infty}$ filtering for a class of uncertain nonlinear time-delay systems,' IEEE Trans. Automat. Control, vol. 48, pp. 1661-1666, 2003 https://doi.org/10.1109/TAC.2003.817012
  5. S. Xu, J. Lam, and Y. Zou, 'H$_{\infty}$ filtering for singular systems,' IEEE Trans. Automat. Control, vol. 48, pp. 2217-2222, 2003 https://doi.org/10.1109/TAC.2003.820149
  6. H. Gao and C. Wang, 'A delay-dependent approach to robust H = filtering for uncertain discrete-time state-delayed systems,' IEEE Trans. Signal Process., vol. 52, pp. 1631-1640, 2004 https://doi.org/10.1109/TSP.2004.827188
  7. M. 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
  8. X. M. Zhang and Q. L. Han, 'Robust H$_{\infty}$ filtering for a class of uncertain linear time-varying delay,' Automatica, vol. 44, pp 157-166, 2008 https://doi.org/10.1016/j.automatica.2007.04.024
  9. E. Fridman and U. Shaked, 'A new H$_{\infty}$ filter design for linear time delay systems,' IEEE Trans. Signal Process., vol. 49, pp. 2839-2843, 2001 https://doi.org/10.1109/78.960431
  10. Z. Wang and K. J. Burnham, 'Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation,' IEEE Trans. Signal Process., vol. 49, pp. 794-804, 2001 https://doi.org/10.1109/78.912924
  11. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-delay Systems, Birkhauser, Boston, 2003
  12. A. Pila, U. Shaked, and C. E. de Souza, 'H$_{\infty}$ filtering for continuous-time linear systems with delay,' IEEE Trans. Automat. Control, vol. 44, pp. 1412-1417, 1999 https://doi.org/10.1109/9.774112
  13. J. H. Kim, S. J. Ahn, and S. Ahn, 'Guaranteed cost and H$_{\infty}$ filtering for discrete-time poly topic uncertain systems with time-delay,' J. Franklin Inst., vol. 342, pp. 365-378, 2005 https://doi.org/10.1016/j.jfranklin.2005.01.002
  14. W. Zhang, L. Yu, and X. Jiang, 'Delay-dependent generalized H$_2$ filtering for uncertain systems with multiple time-varying state delays,' Signal Processing, vol. 87, pp. 709-724, 2007 https://doi.org/10.1016/j.sigpro.2006.07.004
  15. M. S. Mahmoud, 'Delay-dependent H$_{\infty}$ filtering of a class of switched discrete-time state delay systems,' Signal Processing, vol. 88, pp. 2709-2719, 2008 https://doi.org/10.1016/j.sigpro.2008.05.014
  16. Y. He, G. Liu, D. Rees, and M. Wu, 'H$_{\infty}$ filtering for discrete-time systems with time-varying delay,' Signal Processing, vol. 89, pp.275-282, 2009 https://doi.org/10.1016/j.sigpro.2008.08.008
  17. C. E. de Souza, K. A. Barbosa, and M. Fu, 'Robust filtering for uncertain liner discrete-time descriptor systems,' Automatica, vol. 44, pp. 792-798, 2008 https://doi.org/10.1016/j.automatica.2007.07.006
  18. I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, 'H$_{\infty}$ control for descriptor systems: A matrix inequalities approach,' Automatica, vol. 33, pp. 669-673, 1997 https://doi.org/10.1016/S0005-1098(96)00193-8
  19. Z. G. Wu and W. N. 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
  20. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, LMI Control Toolbox, MA, The MathWorks Inc., 1995