Distributed non-fragile filtering for sensor networks with randomly occurring filter gain variations

Abstract

In this paper, the distributed filtering for a class of sensor networks with randomly occurring filter gain variations is investigated, where the additively norm-bounded filter gain variations is addressed. For the filter implementation uncertainties, a set of stochastic variables are firstly employed to indicate random occurrence of the filter gain variation and a set of norm bounds are introduced to measure the variation size. Based on some stochastic analysis method and using the robust control technique, a new sufficient condition is derived such that the filtering error system is asymptotically stable in the mean-square sense and achieves a prescribed $H_{\infty }$ performance level. The optimal filter gains are also obtained and the effectiveness of the proposed design is finally demonstrated via a numerical example.

Keywords:

• $H_{\infty }$ filtering
• non-fragile filtering
• distributed filtering
• random filter gain variations
• sensor networks
• linear matrix inequalities (LMIs)

Acknowledgements

We would like to thank the reviewers and editors of this journal for their valuable comments that has helped to improve the present paper.

Additional information

Funding

This research work was partly supported by the National Natural Science Foundation of China [grant number 61403341], [grant number 61273117]; the Zhejiang Provincial Natural Science Foundation of China [grant number LQ14F030002]; the Zhejiang Qianjiang talent project [grant number QJD1402018]; and the Zhejiang Science and Technology Agency project [grant number 2011D60SA750073], [grant number 2011D60SA750075].