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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 1967875, 7 pages
http://dx.doi.org/10.1155/2016/1967875
Research Article

Positive Filtering with -Gain for Discrete-Time Positive Systems

College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 7 March 2016; Revised 30 March 2016; Accepted 7 April 2016

Academic Editor: Carmen Coll

Copyright © 2016 Xiaoming Chen. 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 positive filtering problem for discrete-time positive systems under the -induced performance. We aim to propose a pair of positive filters with error-bounding features to estimate the output of positive systems. A novel characterization is first constructed so that the filtering error system is asymptotically stable with a prescribed -induced performance. Then, necessary and sufficient conditions for the existence of required filters are presented, and the obtained results are expressed as linear programming problems. Moreover, it is pointed out that the results can be easily checked by standard software. In addition, a numerical example is given to show the effectiveness of the proposed design procedures.