Journal of Applied Mathematics
Volume 2012 (2012), Article ID 710904, 11 pages
http://dx.doi.org/10.1155/2012/710904
Research Article

Finite-Time 𝐻 ∞ Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations

Huihong Zhao1 and Chenghui Zhang2

1Department of Electromechanical Engineering, Dezhou University, No. 566 University Road West, Dezhou 253023, China
2School of Control Science and Engineering, Shandong University, 17923 Jingshi Road, Jinan 250061, China

Received 29 March 2012; Revised 3 June 2012; Accepted 6 June 2012

Academic Editor: Qiang Ling

Copyright © 2012 Huihong Zhao and Chenghui Zhang. 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 is concerned with the finite-time 𝐻 ∞ filtering problem for linear continuous time-varying systems with uncertain observations and ℒ2-norm bounded noise. The design of finite-time 𝐻 ∞ filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time 𝐻 ∞ filtering problem is solved. A numerical example is given to illustrate the performance of the 𝐻 ∞ filter.