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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 382756, 7 pages
Research Article

Control Design of Detectable Periodic Markov Jump Systems

1College of Mathematics and Systems Science, State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China
2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received 22 May 2015; Accepted 6 September 2015

Academic Editor: Leonid Shaikhet

Copyright © 2015 Ting Hou and Hongji Ma. 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.


An infinite horizon control problem is addressed for discrete-time periodic Markov jump systems with -dependent noise. Above all, by use of the spectral criterion of detectability, an extended Lyapunov stability theorem is developed for the concerned dynamics. Further, based on a game theoretic approach, a state-feedback control design is proposed. It is shown that under the condition of detectability feedback gain can be constructed through the solution of a group of coupled periodic difference equations.