All H∞ singular and normal filter design for uncertain singular systems

Authors:
Xu Tianqun;Chen Yuepeng;Zhang Jingxin;Liu Huanbin;Xu Tianhe
Affiliations:
School of Science, Wuhan University of Technology, Wuhan, China;School of Automation, Wuhan University of Technology, Wuhan, China;Electrical and Computer Systems Engineering, Monash University, Australia;Department of Mathematics, Huanggang Normal University, Huanggang, China;School of Geodesy and Geomatics, Wuhan University, Wuhan, China and Xi'an Research Institute of Surveying and Mapping, Xi'an, China
Venue:
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Year:
2009

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Abstract

In this short paper, the H∞ filter design for uncertain singular systems is considered. We study to design normal filters and singular filters for the same singular systems. Via using linear matrix inequalities (LMIs), the sufficient conditions are established for the existences of two kinds of filter forms such that two uncertain error systems are admissible and their transfer functions from the disturbance to the filtering error output satisfy a prescribed H∞-norn bound constraint. By solving LMIs, explicit parameterization expressions of all desired normal filters and singular filters are obtained. Furthermore, all results involve no decomposition the original singular system matrices. It makes that the procedure of filter design is simple and direct. Simultaneously, we still optimize and compare with their H∞ performances for uncertain error systems under two kinds of filter cases. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method and compare with their H∞ performances.