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Mathematical Problems in Engineering
Volume 2013, Article ID 579137, 9 pages
Research Article

Filter Design with Minimum Entropy for Continuous-Time Linear Systems

1School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway
3Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, China
4Information Overall Department, North Information Control Group Co., Ltd., Nanjing 211153, China

Received 1 August 2013; Revised 8 October 2013; Accepted 21 October 2013

Academic Editor: Zhiguang Feng

Copyright © 2013 Jie Zhang 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.


We deal with the design problem of minimum entropy filter in terms of linear matrix inequality (LMI) approach for linear continuous-time systems with a state-space model subject to parameter uncertainty that belongs to a given convex bounded polyhedral domain. Given a stable uncertain linear system, our attention is focused on the design of full-order and reduced-order robust minimum entropy filters, which guarantee the filtering error system to be asymptotically stable and are required to minimize the filtering error system entropy (at ) and to satisfy a prescribed disturbance attenuation performance. Sufficient conditions for the existence of desired full-order and reduced-order filters are established in terms of LMIs, respectively, and the corresponding filter synthesis is cast into a convex optimization problem which can be efficiently handled by using standard numerical software. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.