H∞ Filter Design for Uncertain Discrete-Time Singular Systems via Normal Transformation

This paper concerns the robust H∞ filtering problem for discrete-time singular systems with norm-bounded uncertainties. Based on the admissibility assumption of singular systems, a set of necessary and sufficient conditions for the existence of the desired filters is established, and a normal filter design method under the linear matrix inequality framework is developed. A numerical example is given to illustrate the application of the proposed method.

[1]  Zhi-Quan Luo,et al.  Multivariate Nonnegative Quadratic Mappings , 2003, SIAM J. Optim..

[2]  Shengyuan Xu,et al.  Robust stabilization for generalized state-space systems with uncertainty , 1999 .

[3]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[4]  Shengyuan Xu,et al.  H∞ filtering for singular systems , 2003, IEEE Trans. Autom. Control..

[5]  K. Grigoriadis,et al.  Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[6]  T. Katayama,et al.  A generalized Lyapunov theorem for descriptor system , 1995 .

[7]  R. M. Palhares,et al.  Robust H/sub /spl infin// filtering design with pole constraints for discrete-time systems: an LMI approach , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[8]  P. Peres,et al.  LMI approach to the mixed H/sub 2//H/sub /spl infin// filtering design for discrete-time uncertain systems , 2001 .

[9]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[10]  Chengwu Yang,et al.  H∞ state feedback control for discrete singular systems , 2000, IEEE Trans. Autom. Control..

[11]  F. Amato,et al.  A note on quadratic stability of uncertain linear discrete-time systems , 1998, IEEE Trans. Autom. Control..

[12]  M. Safonov,et al.  Hankel model reduction without balancing-A descriptor approach , 1987, 26th IEEE Conference on Decision and Control.

[13]  Shengyuan Xu,et al.  Robust stability and stabilization of discrete singular systems: an equivalent characterization , 2004, IEEE Transactions on Automatic Control.

[14]  L. Dai.  Observers for discrete singular systems , 1988 .

[15]  Dong Yue,et al.  Robust H/sub /spl infin// filter design of uncertain descriptor systems with discrete and distributed delays , 2004, IEEE Transactions on Signal Processing.

[16]  Anke Xue,et al.  Robust H∞ Filtering for a Class of Uncertain Lurie Time-delay Singular Systems , 2007 .

[17]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[18]  Y. Hung,et al.  Robust mixed H/sub 2//H/sub /spl infin// filtering with regional pole assignment for uncertain discrete-time systems , 2002 .

[19]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[20]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[21]  Andrew Packard,et al.  Robust H2 and H∞ filters for uncertain LFT systems , 2005, IEEE Trans. Autom. Control..