Circuits, Systems, and Signal Processing

, Volume 33, Issue 11, pp 3635–3648 | Cite as

Design of An Arcak-Type Generalized \(H_2\) Filter for Delayed Static Neural Networks

Short Paper
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Abstract

In this paper, an Arcak-type generalized \(H_2\) filter is designed for a class of static neural networks with time-varying delay. By employing some inequalities and constructing a suitable Lyapunov functional, a delay-dependent condition is derived by means of linear matrix inequalities such that the filtering error system is globally asymptotically stable and a prescribed generalized \(H_2\) performance is achieved. It is shown that the design of such a desired filter for a delayed static neural network is successfully transformed into solving a convex optimization problem subject to some linear matrix inequalities. It is thus facilitated readily by some standard algorithms. A numerical example is finally provided to show the effectiveness of the developed approach. A comparison on the generalized \(H_2\) performance for different gain parameters of the activation function is also given.

Keywords

Static neural networks Arcak-type filter design Generalized \(H_2\) performance Time delay Gain parameters 
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Notes

Acknowledgments

The authors would like to thank the associate editor and anonymous reviewers for their valuable comments that have greatly improved the quality of this paper. The work was supported by the National Natural Science Foundation of China under Grant No. 61005047, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010214. Also, this publication was made possible by NPRP grant #4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the author[s].

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Electronics and Information EngineeringSoochow UniversitySuzhou People’s Republic of China
  2. 2.Texas A&M University at QatarDohaQatar

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