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Mathematical Problems in Engineering
Volume 2013, Article ID 574571, 8 pages
Research Article

Robust Filtering for a Class of Uncertain Markovian Jump Systems with Time Delays

Yi Yang1,2 and Junwei Lu3

1Reliability and Systems Engineering School, Beihang University, Beijing 100191, China
2China Astronaut Research and Training Center, Beijing 100094, China
3School of Electrical and Automation Engineering, Nanjing Normal University, 78 Bancang Street, Nanjing 210042, China

Received 5 May 2013; Accepted 1 July 2013

Academic Editor: Jun Hu

Copyright © 2013 Yi Yang and Junwei Lu. 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.


This paper studies the problem of robust filtering for a class of uncertain time-delay systems with Markovian jumping parameters. The system under consideration is subject to norm-bounded time-varying parameter uncertainties. The problem to be addressed is the design of a Markovian jump filter such that the filter error dynamics are stochastically stable and a prescribed bound on the -induced gain from the noise signals to the filter error is guaranteed for all admissible uncertainties. A sufficient condition for the existence of the desired robust filter is given in terms of two sets of coupled algebraic Riccati inequalities. When these algebraic Riccati inequalities are feasible, the expression of a desired filter is also presented. Finally, an illustrative numerical example is provided.