Mixed H2/Hinfinity deconvolution of uncertain periodic FIR channels

Abstract The deconvolution problem is to design a deconvolution filter that reconstructs a signal from the noise corrupted measurement output of a signal transmission channel. In this paper, we consider the deconvolution problem for uncertain periodic FIR transmission channels. The uncertainty appears in the channel coefficients and is norm bounded. The aim is to design an optimal H2 deconvolution filter subject to an H∞ performance constraint. A solution to this mixed H2/H∞ problem is given in terms of linear matrix inequalities. An advantage of the linear matrix inequality solution is in its computational efficiency using standard software.

[1]  Zi-Li Deng,et al.  Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems , 1996, Autom..

[2]  C. Sidney Burrus,et al.  A unified analysis of multirate and periodically time-varying digital filters , 1975 .

[3]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[4]  Michael J. Grimble,et al.  H ∞ optimal multichannel linear deconvolution filters, predictors and smoothers , 1996 .

[5]  Bassam Bamieh,et al.  The H 2 problem for sampled-data systems m for sampled-data systems , 1992 .

[6]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

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

[8]  B. Francis,et al.  Optimal Sampled-data Control , 1995 .

[9]  Bassam Bamieh,et al.  The 2 problem for sampled-data systems , 1992, Systems & Control Letters.

[10]  Ryohei Ishii,et al.  A design method for a periodically time-varying digital filter for spectrum scrambling , 1990, IEEE Trans. Acoust. Speech Signal Process..

[11]  Luigi Chisci,et al.  MMSE deconvolution via polynomial methods and its dual LQG regulation , 1994, Autom..

[12]  Ching-An Lin,et al.  A unified approach to scrambling filter design , 1995, IEEE Trans. Signal Process..

[13]  Cishen Zhang,et al.  Analysis of H2 and H∞ performance of discrete periodically time-varying controllers , 1997, Autom..

[14]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[15]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[16]  K. Poolla,et al.  Robust control of linear time-invariant plants using periodic compensation , 1985 .

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

[18]  James S. Prater,et al.  Analysis and design of periodically time-varying IIR filters, with applications to transmultiplexing , 1992, IEEE Trans. Signal Process..

[19]  M. Bellanger.  Adaptive filter theory: by Simon Haykin, McMaster University, Hamilton, Ontario L8S 4LB, Canada, in: Prentice-Hall Information and System Sciences Series, published by Prentice-Hall, Englewood Cliffs, NJ 07632, U.S.A., 1986, xvii+590 pp., ISBN 0-13-004052-5 025 , 1987 .

[20]  Lihua Xie,et al.  On the Discrete-time Bounded Real Lemma with application in the characterization of static state feedback H ∞ controllers , 1992 .