Browse > Article

Reduced-order Parameter-dependent Robust $H_{\infty}$ Filtering for Discrete Uncertain Singular Systems  

Kim, Jong-Hae (Department of Electronic Eng., Sun Moon University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SC / v.48, no.5, 2011 , pp. 59-65 More about this Journal
Abstract
In this paper, we present a reduced-order parameter-dependent robust $H_{\infty}$ filter design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for parameter-dependent singular systems is derived from a parameter-dependent Lyapunov function. On the basis of the obtained BRL, low order robust $H_{\infty}$ filter design method is presented by polytopic approach, new reduced-order method, and LMI(linear matrix inequality) technique. Finally, a numerical example is presented to illustrated the feasibility of the proposed method.
Keywords
Reduced-order filter; $H_{\infty}$ filter; parameter-dependence; discrete singular systems; LMI;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA, SIAM, 1994.
2 M. C. de Oliverira, J. Bernussou, and C. Geromel, "A new discrete-time robust stability condition," Systems and Control Letters, vol. 37, pp. 261-265, 1999.   DOI   ScienceOn
3 J. Zhang, Y. Xia, and P. Shi, "Parameter -dependent robust $H_{{\infty}}$ filtering for uncertain discrete-time systems," Automatica, vol. 45, pp. 506-565, 2009.
4 K. M. Grigoriadis and J. T. Watson, "Reduced-order $H_{{\infty}}$ and $L_2-L{\infty}$ filtering via linear matrix inequalities," IEEE Transactions on Aerospace Electron Systems, vol. 33, pp. 1326-1338, 1997.   DOI
5 J. L. Rawson, C. S. Hsu, and H. Rho, "Reduced order $H_{{\infty}}$ filters for discrete linear systems," Proceedings of Conference on Decision and Control, San Diego, CA, USA, pp. 3311-3316, 1997.
6 S. Xu and T. Chen, "Reduced-order $H_{{\infty}}$ filtering for stochastic systems," IEEE Transactions on Signal Processing, vol. 50, pp. 2998-3007, 2002.   DOI   ScienceOn
7 M. Darouach. M. Zasadzinski, and M. Hayar, "Reduced-order observer design for descriptor systems with unknown inputs," IEEE Transactions on Automatic Control, vol. 41, pp. 1068-1072, 1996.   DOI   ScienceOn
8 L. Syrmos "Observer design for descriptor systems with unmeasurable disturbances," Proceedings of Conference on Decision and Control, Tucson, Arizona, USA, pp. 981-982, 1992.
9 S. Xu and J. Lam, "Reduced-order $H_{{\infty}}$ filtering for singular systems," Systems and Control Letters, vol. 56, pp.48-57, 2007.   DOI   ScienceOn
10 S. Xu and J. Lam, "Robust stability and stabilization of discrete singular systems: an equivalent characterization," IEEE Transactions on Automatic Control, vol. 49, pp. 568-574, 2004.   DOI   ScienceOn
11 A. Elsayed and M. Grimble, "A new approach to $H_{{\infty}}$ design for optimal digital linear filters," IMA Journal of Mathematical Control and Information, vol. 6, pp. 233-251, 1989.   DOI
12 H. Gao, J. Lam, P. Shi, and C. Wang, "New approach to mixed $H_2/H{\infty}$ filtering for polytopic discrete-time systems," IEEE Transactions on Signal Processing, vol. 52, pp. 1631-1640, 2004.   DOI
13 H. Gao, J. Lam, P. Shi, and C. Wang, "Parameter-dependent filter design with guaranteed $H_{{\infty}}$ performance," IEE Proceedings Control Theory and Applications, vol. 152, pp. 531-537, 2005.   DOI
14 Y. Chen, Z. Zhou, C. Zeng, and Q. Zhang, "$H_{{\infty}}$ filtering for descriptor systems," International Journal of Control, Automation, and Systems, vol. 4, pp. 697-704, 2006.
15 C. M. Lee and I. K. Fong, "$H_{{\infty}}$ optimal singular and normal filter design for uncertain singular systems," IET Control Theory and Applications, vol. 1, pp. 119-126, 2007.   DOI
16 L. Dai, Singular Control Systems, Berlin, Springer-Verlag, 1989.
17 B. D. O. Anderson and J. B. Moore, Optimal Filtering, Prentice-Hall, Englewood Cliffs, 1979.
18 S. Xu and J. Lam, Robust Control and Filtering of Singular Systems, Berlin, Springer-Verlag, 2006.