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Robust exponential passive filtering for uncertain neutral-type neural networks with time-varying mixed delays via Wirtinger-based integral inequality

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  • Control Theory and Applications
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Abstract

This paper is concerned with the problem of the robust exponential passive filter design for uncertain neutral-type neural networks with time-varying mixed delays. Our aim is to design a Luenberger-type filter for estimating information about the neuron states, which is required in some applied areas. By constructing an appropriate Lyapunov-Krasovskii functional and using the Wirtinger-based integral inequality to estimate its derivative, a delay-range-dependent and delay-rate-dependent criterion is presented to ensure the augmented filtering dynamic system to be robustly exponentially stable and passive with an expected dissipation. Since the criterion is presented in the form of linear matrix inequalities with nonlinear constraints, a cone complementarity linearization algorithm is proposed to determine the filter gain from solution to the nonlinear problem. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    Xian Zhang, XiaoFei Fan, Yu Xue & YanTao Wang

  2. Department of Finance, Heilongjiang University, Harbin, 150080, China

    Wei Cai

Authors
  1. Xian Zhang
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  2. XiaoFei Fan
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  3. Yu Xue
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  4. YanTao Wang
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Corresponding author

Correspondence to Xian Zhang.

Additional information

Recommended by Associate Editor Xiaojie Su under the direction of Editor Euntai Kim. This work was partially supported by the National Natural Science Foundation of China (11371006), the Natural Science Foundation of Heilongjiang Province (F201326 and A201416), the Fund of Heilongjiang Education Committee (12541603).

Xian Zhang received his Ph.D. degree in Control Theory from Queen’s University of Belfast in UK in 2004. Since 2004 he has been at Heilongjiang University, where he is currently a Professor in the School of Mathematical Science. His current research interests include neural networks, genetic regulatory networks, mathematical biology and stability analysis of delayed dynamic systems. He has received the Second Class of Science and Technology Awards of Heilongjiang Province in 2005 and the Three Class of Science and Technology Awards of Heilongjiang Province in 2015. He is a member of the IEEE, and a Vice President of Mathematical Society of Heilongjiang Province. Since 2006, he served as an Editor of the Journal of Natural Science of Heilongjiang University. He has authored more than 100 research papers.

Xiaofei Fan was born in Inner Mongolia, China, in 1991. She received the B.S. degree in School of Mathematical Science from Hulunbeir College, Hulunbeir, China, in 2014. She is currently an M.S. student in Heilongjiang University, Harbin, China. Her research interests include genetic regulatory networks and stability analysis of delayed dynamic systems.

Yu Xue received the B.S. degree in Automation from Harbin University of Science and Technology, China in 2002; the PhD degree in Control Theory and Control Engineering from Harbin Institute of Technology, China in 2007. From April 2007 to August 2009, she is an Engineer in Sichuan Academy of Aerospace Technology. From September 2009 to May 2013, she is a Senior Engineer in Sichuan Academy of Aerospace Technology. In June 2013, she joined Heilongjiang University. Her research interests include stability analysis of delayed dynamic systems, robust control and genetic regulatory networks.

Yantao Wang received the B.S. degree from School of Mathematical Science, Heilongjiang University, Harbin, China, in 1994; the M.E. degree from School of Mathematical Science, Heilongjiang University, Harbin, China, in 2005; her current research interests include neural networks, genetic regulatory networks, mathematical biology and stability analysis of delayed dynamic systems.

Wei Cai received the Master degree in Commerce from the University of Sydney, Australia in 2007. From 2007 to 2008, she worked as a data analyst in Deloitte Touche Tohmatsu CPA Led. Beijing branch. In 2008, she began to work in the department of finance in Heilongjiang University. Her research interests include using modern techniques in mathematical and logical analysis area.

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Zhang, X., Fan, X., Xue, Y. et al. Robust exponential passive filtering for uncertain neutral-type neural networks with time-varying mixed delays via Wirtinger-based integral inequality. Int. J. Control Autom. Syst. 15, 585–594 (2017). https://doi.org/10.1007/s12555-015-0441-0

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  • DOI: https://doi.org/10.1007/s12555-015-0441-0

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