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Mathematical Problems in Engineering
Volume 2016, Article ID 2134807, 9 pages
Research Article

Positive State-Bounding Observer Design for Positive Interval Markovian Jump Systems

Institute of Systems Science, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning 110819, China

Received 3 May 2016; Accepted 10 October 2016

Academic Editor: Guangming Xie

Copyright © 2016 Di 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.


This paper studies the problem of positive state-bounding observer design for a class of positive Markovian jump systems with interval parameter uncertainties by a linear programming approach. For the first, necessary and sufficient conditions are obtained for stochastic stability and performance of positive Markovian jump systems by an “equivalent” deterministic positive linear system. Furthermore, based on the results obtained in this paper, sufficient conditions for the existence of the positive state-bounding observer are derived. The conditions can be solved in terms of linear programming. Finally, a numerical example is used to illustrate the effectiveness of the results obtained.