American Institute of Mathematical Sciences

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April  2011, 7(2): 283-289. doi: 10.3934/jimo.2011.7.283

New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays

Zhigang Zeng 1, and  Tingwen Huang 2,

1. 

Department of Control Science & Engineering, Huazhong University of Science & Technology, and Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, Hubei 430074, China
2. 

Texas A&M University at Qatar, Doha, P.O. Box 5825, Qatar, United States

Received  December 2009 Revised  September 2010 Published  April 2011

In this paper, by using some analytic techniques, several sufficient conditions are given to ensure the passivity of continuous-time recurrent neural networks with delays. The passivity conditions are presented in terms of some negative semi-definite matrices. They are easily verifiable and easier to check computing with some conditions in terms of complicated linear matrix inequality.
Keywords: Passivity, linear matrix inequality., neural networks, negative semi-definite matrix, delays.
Mathematics Subject Classification: Primary: 34A25, 34A34; Secondary: 15A2.
Citation: Zhigang Zeng, Tingwen Huang. New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays. Journal of Industrial & Management Optimization, 2011, 7 (2) : 283-289. doi: 10.3934/jimo.2011.7.283
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show all references

References:
[1]

Automatica, 33 (1996), 635-641. doi: 10.1016/S0005-1098(96)00180-X.  Google Scholar

[2]

IEEE Transactions on Robotics, 24 (2008), 416-429. doi: 10.1109/TRO.2008.915438.  Google Scholar

[3]

Journal of Industrial and Management Optimization, 5 (2009), 867-880. doi: 10.3934/jimo.2009.5.867.  Google Scholar

[4]

IEEE Transactions on Circuits and Systems-II: Express Briefs, 52 (2005), 471-475. Google Scholar

[5]

Journal of Industrial and Management Optimization, 4 (2008), 817-826.  Google Scholar

[6]

Physical Review E, 68 (2003), 1-7. doi: 10.1103/PhysRevE.68.016118.  Google Scholar

[7]

Neurocomputing, 70 (2007), 1071-1078. Google Scholar

[8]

Springer-Verlag, London, U.K., 2000. Google Scholar

[9]

Journal of Mathematical Analysis and Applications, 292 (2004), 247-258. doi: 10.1016/j.jmaa.2003.11.055.  Google Scholar

[10]

Chaos, Solitons and Fractals, 34 (2007), 1546-1551. doi: 10.1016/j.chaos.2005.04.124.  Google Scholar

[11]

Journal of Process Control, 18 (2008), 515-526. doi: 10.1016/j.jprocont.2007.07.007.  Google Scholar

[12]

IEEE Transactions on Circuits and Systems-II: Express Briefs, 54 (2007), 161-165. doi: 10.1109/TCSII.2006.886464.  Google Scholar

[13]

Industrial & Engineering Chemistry Research, 47 (2008), 4765-4774. doi: 10.1021/ie070599c.  Google Scholar

[14]

Journal of Industrial and Management Optimization, 4 (2008), 33-52.  Google Scholar

[15]

Journal of Industrial and Management Optimization, 1 (2005), 389-404.  Google Scholar

[16]

Journal of Industrial and Management Optimization, 1 (2005), 415-432.  Google Scholar

[17]

IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 48 (2001), 256-259. doi: 10.1109/81.904893.  Google Scholar

[18]

IEEE Transactions on Neural Networks, 12 (2001), 412-417. doi: 10.1109/72.914535.  Google Scholar

[19]

IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173-178. Google Scholar

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