# American Institute of Mathematical Sciences

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

 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.
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
##### References:
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##### References:
 [1] S. Commuri and F. L. Lewis, CMAC neural networks for control of nonlinear dynamical systems: structure, stability and passivity, Automatica, 33 (1996), 635-641. doi: 10.1016/S0005-1098(96)00180-X.  Google Scholar [2] A. Kugi, C. Ott, A. Albu-Schaffer and G. Hirzinger, On the passivity-based impedance control of flexible joint robots, IEEE Transactions on Robotics, 24 (2008), 416-429. doi: 10.1109/TRO.2008.915438.  Google Scholar [3] J. Li, H. R. Feng and M.C. Wang, A replenishment policy with defective products, backlog and delay of payments, Journal of Industrial and Management Optimization, 5 (2009), 867-880. doi: 10.3934/jimo.2009.5.867.  Google Scholar [4] C. G. Li and X. F. Liao, Passivity analysis of neural networks with time delay, IEEE Transactions on Circuits and Systems-II: Express Briefs, 52 (2005), 471-475. Google Scholar [5] L. Lin, D. He and Z. Y. Tan, Bounds on delay start lpt algorithm for scheduling on two identical machines in the l(p) norm, Journal of Industrial and Management Optimization, 4 (2008), 817-826.  Google Scholar [6] X. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay, Physical Review E, 68 (2003), 1-7. doi: 10.1103/PhysRevE.68.016118.  Google Scholar [7] X. Y. Lou and B. T. Cui, Passivity analysis of integro-differential neural networks with time-varying delays, Neurocomputing, 70 (2007), 1071-1078. Google Scholar [8] R. Lozano, B. Brogliato, O. Egeland and B. Maschke, "Systems Analysis and Control: Theory and Applications, Dissipative," Springer-Verlag, London, U.K., 2000. Google Scholar [9] M. S. Mahmoud and A. Ismail, Passivity and passification of time-delay systems, Journal of Mathematical Analysis and Applications, 292 (2004), 247-258. doi: 10.1016/j.jmaa.2003.11.055.  Google Scholar [10] J. H. Park, Further results on passivity analysis of delayed cellular neural networks, Chaos, Solitons and Fractals, 34 (2007), 1546-1551. doi: 10.1016/j.chaos.2005.04.124.  Google Scholar [11] O. J. Rojas, J. Bao and P. L. Lee, On dissipativity, passivity and dynamic operability of nonlinear processes, Journal of Process Control, 18 (2008), 515-526. doi: 10.1016/j.jprocont.2007.07.007.  Google Scholar [12] J. J. Rubio and W. Yu, Stability analysis of nonlinear system identification via delayed neural networks, IEEE Transactions on Circuits and Systems-II: Express Briefs, 54 (2007), 161-165. doi: 10.1109/TCSII.2006.886464.  Google Scholar [13] H. Santoso, J. Bao and P. L. Lee, Dynamic operability analysis for stable and unstable linear processes, Industrial & Engineering Chemistry Research, 47 (2008), 4765-4774. doi: 10.1021/ie070599c.  Google Scholar [14] S. Wang, Q. Shao and X. Zhou, Knot-optimizing spline networks (KOSNETS) for nonparametric regression, Journal of Industrial and Management Optimization, 4 (2008), 33-52.  Google Scholar [15] L. X. Xu and W. Q. Liu, A new recurrent neural network adaptive approach for host-gate way rate control protocol within intranets using ATM ABR service, Journal of Industrial and Management Optimization, 1 (2005), 389-404.  Google Scholar [16] Y. Yatsenko and N. Hritonenko, Optimization of the lifetime of capital equipment using integral models, Journal of Industrial and Management Optimization, 1 (2005), 415-432.  Google Scholar [17] W. Yu and X. Li, Some stability properties of dynamic neural networks, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 48 (2001), 256-259. doi: 10.1109/81.904893.  Google Scholar [18] W. Yu and X. Li, New results on system identification with dynamic neural networks, IEEE Transactions on Neural Networks, 12 (2001), 412-417. doi: 10.1109/72.914535.  Google Scholar [19] W. Yu, Passivity analysis for dynamic multilayer neuro identifier, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173-178. Google Scholar
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