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Mathematical Problems in Engineering
Volume 2013, Article ID 426271, 9 pages
Research Article

Control for the Continuous-Time Markovian Jump Linear Uncertain Systems with Partly Known Transition Rates and Input Quantization

1State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
2College of Information Science and Engineering, Northeastern University, Shenyang 110189, China

Received 22 May 2013; Accepted 19 July 2013

Academic Editor: Bochao Zheng

Copyright © 2013 Xin-Gang Zhao 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.


For a class of continuous-time Markovian jump linear uncertain systems with partly known transition rates and input quantization, the state-feedback control design is considered. The elements in the transition rates matrix include completely known, boundary known, and completely unknown ones. First, an cost index for Markovian jump linear uncertain systems is introduced; then by introducing a new matrix inequality condition, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs) for the control of the Markovian jump linear uncertain systems. Less conservativeness is achieved than the result obtained with the existing technique. Finally, a numerical example is given to verify the validity of the theoretical results.