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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 8085327, 12 pages
http://dx.doi.org/10.1155/2016/8085327
Research Article

Positive Observer Design for Positive Delayed Markovian Jump Systems

School of Information and Control Engineering, Liaoning Shihua University, Fushun, Liaoning 113001, China

Received 20 April 2016; Revised 20 June 2016; Accepted 29 June 2016

Academic Editor: Rigoberto Medina

Copyright © 2016 Guoliang Wang. 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

The positive observer design problem is considered for a class of positive delayed Markovian jump systems (PDMJSs). Firstly, a necessary and sufficient condition is established to check the positivity of delayed Markovian jump systems (DMJSs). Then, necessary and sufficient conditions for PDMJSs being asymptotically mean stable are established to be independent of time delay. Based on the proposed results, sufficient conditions for the existence of the desired positive observer gains including mode-independent case are provided. Additionally, more general cases that transition rate matrix (TRM) is partially unknown or uncertain are considered, respectively. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.