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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 953831, 10 pages
http://dx.doi.org/10.1155/2015/953831
Research Article

Index for Stochastic Linear Discrete-Time Systems

1College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
2College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China

Received 26 January 2015; Accepted 20 April 2015

Academic Editor: Zidong Wang

Copyright © 2015 Yan Li 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 discusses the index problem for stochastic linear discrete-time systems. A necessary and sufficient condition of index is given for such systems in finite horizon. It is proved that when the index is greater than a given value, the feasibility of index is equivalent to the solvability of a constrained difference equation. The above result can be applied to the fault detection observer design. Finally, some examples are presented to illustrate the proposed theoretical results.