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Relaxed H ∞ Controller Design for Continuous Markov Jump System with Incomplete Transition Probabilities

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Abstract

This paper studies the H ∞ state feedback control of continuous-time Markov jump linear systems (MJLSs) with incomplete transition probabilities (TPs) which are allowed to be known, uncertain with known lower and upper bounds, and completely unknown. Combining the TP property and a matrix transformation technique, a new method for the H ∞ controller synthesis is proposed in terms of linear matrix inequalities (LMIs). The dominant feature of the proposed method is that two sets of slack variables without coupling relationship are introduced. It is shown that the proposed method is less conservative than the existing result. The effectiveness of the proposed method is further illustrated by numerical examples.

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Acknowledgements

The authors would like to thank the Editor, the Associate Editor, and the three anonymous reviewers for their valuable comments and suggestions, which have helped to significantly improve the quality and presentation of this paper. This work was supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20130949), the Natural Science Foundation of Jiangsu Provincial Universities of China (No. 13KJB120004), the Jiangsu provincial science and technology support project (No. BE2011188), the 2012 Qing Lan Project of Jiangsu Province, the National Natural Science Foundation of China (Nos. 61273155, 61322312, 51205185), and New Century Excellent Talents in University (No. NCET-11-0083).

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Authors and Affiliations

  1. College of Automation and Electrical Engineering, Nanjing University of Technology, Nanjing, 211816, China

    Mouquan Shen, Guangming Zhang & Yuhao Yuan

  2. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Dan Ye

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  1. Mouquan Shen
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Correspondence to Mouquan Shen.

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Shen, M., Zhang, G., Yuan, Y. et al. Relaxed H ∞ Controller Design for Continuous Markov Jump System with Incomplete Transition Probabilities. Circuits Syst Signal Process 33, 1393–1410 (2014). https://doi.org/10.1007/s00034-013-9695-z

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  • DOI: https://doi.org/10.1007/s00034-013-9695-z

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