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Journal of Applied Mathematics
Volume 2012, Article ID 615790, 16 pages
http://dx.doi.org/10.1155/2012/615790
Research Article

Finite-Time 𝐻∞ Filtering for Singular Stochastic Systems

College of Science, Henan University of Technology, Zhengzhou 450001, China

Received 14 July 2011; Revised 5 November 2011; Accepted 5 November 2011

Academic Editor: F. MarcellΓ‘n

Copyright Β© 2012 Caixia Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper addresses the problem of finite-time 𝐻∞ filtering for one family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Initially, the definitions of singular stochastic finite-time boundedness and singular stochastic 𝐻∞ finite-time boundedness are presented. Then, the 𝐻∞ filtering is designed for the class of singular stochastic systems with or without uncertain parameters to ensure singular stochastic finite-time boundedness of the filtering error system and satisfy a prescribed 𝐻∞ performance level in some given finite-time interval. Furthermore, sufficient criteria are presented for the solvability of the filtering problems by employing the linear matrix inequality technique. Finally, numerical examples are given to illustrate the validity of the proposed methodology.