Browse > Article

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

Kim, Jong-Hae (선문대학교 전자공학과)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.58, no.9, 2009 , pp. 1796-1801 More about this Journal
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
Robust $H_{\infty}$ filtering; Descriptor systems; Delay-dependent approach; LMI;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-delay Systems, Birkhauser, Boston, 2003
2 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   DOI   ScienceOn
3 P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, LMI Control Toolbox, MA, The MathWorks Inc., 1995
4 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   DOI   ScienceOn
5 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   DOI   ScienceOn
6 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   DOI   ScienceOn
7 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   DOI   ScienceOn
8 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   DOI   ScienceOn
9 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   DOI   ScienceOn
10 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   DOI   ScienceOn
11 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   DOI   ScienceOn
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   DOI   ScienceOn
13 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   DOI   ScienceOn
14 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   DOI   ScienceOn
15 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   DOI   ScienceOn
16 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   DOI   ScienceOn
17 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   DOI
18 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   DOI   ScienceOn
19 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   DOI   ScienceOn
20 S. Xu, J. Lam, and Y. Zou, 'H$_{\infty}$ filtering for singular systems,' IEEE Trans. Automat. Control, vol. 48, pp. 2217-2222, 2003   DOI   ScienceOn