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Dissipativity Analysis and Stabilization for Stochastic Systems with Repeated Scalar Nonlinearities and Applications

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Abstract

This paper investigates the problem of exponential dissipativity for stochastic systems with repeated scalar nonlinearities. The nonlinear system is described by a state equation containing a repeated scalar nonlinearity, which typically appears in recurrent neural networks. Attention is focused on the exponential dissipativity analysis of stochastic systems with repeated scalar nonlinearities with respect to quadratic supply rates. Passive and non-expansive property of stochastic systems with repeated scalar nonlinearities is also characterized. Moreover, a controller has been designed to make the stochastic systems with repeated scalar nonlinearities asymptotically stable. A Marketing-Production system and a Chua circuit are given to illustrate the effectiveness of the proposed design method.

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Acknowledgements

The work is supported by the Natural Science Foundation of China under Grants 60974021 and 61125303, the 973 Program of China under Grant 2011CB710606, the Fund for Distinguished Young Scholars of Hubei Province under Grant 2010CDA081.

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Authors and Affiliations

  1. School of Information Engineering, Nanchang Hangkong University, Nanchang, 330063, China

    Cihui Yang

  2. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhigang Zeng & Shiping Wen

  3. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, 430074, China

    Zhigang Zeng & Shiping Wen

Authors
  1. Cihui Yang
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  2. Zhigang Zeng
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  3. Shiping Wen
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Correspondence to Zhigang Zeng.

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Yang, C., Zeng, Z. & Wen, S. Dissipativity Analysis and Stabilization for Stochastic Systems with Repeated Scalar Nonlinearities and Applications. Circuits Syst Signal Process 31, 2019–2033 (2012). https://doi.org/10.1007/s00034-012-9431-0

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  • DOI: https://doi.org/10.1007/s00034-012-9431-0

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