American Institue of Mathematical Sciences

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:
 [1] S. Commuri and F. L. Lewis, CMAC neural networks for control of nonlinear dynamical systems: structure, stability and passivity,, Automatica, 33 (1996), 635. doi: 10.1016/S0005-1098(96)00180-X. [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. doi: 10.1109/TRO.2008.915438. [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. doi: 10.3934/jimo.2009.5.867. [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. [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. [6] X. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay,, Physical Review E, 68 (2003), 1. doi: 10.1103/PhysRevE.68.016118. [7] X. Y. Lou and B. T. Cui, Passivity analysis of integro-differential neural networks with time-varying delays,, Neurocomputing, 70 (2007), 1071. [8] R. Lozano, B. Brogliato, O. Egeland and B. Maschke, "Systems Analysis and Control: Theory and Applications, Dissipative,", Springer-Verlag, (2000). [9] M. S. Mahmoud and A. Ismail, Passivity and passification of time-delay systems,, Journal of Mathematical Analysis and Applications, 292 (2004), 247. doi: 10.1016/j.jmaa.2003.11.055. [10] J. H. Park, Further results on passivity analysis of delayed cellular neural networks,, Chaos, 34 (2007), 1546. doi: 10.1016/j.chaos.2005.04.124. [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. doi: 10.1016/j.jprocont.2007.07.007. [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. doi: 10.1109/TCSII.2006.886464. [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. doi: 10.1021/ie070599c. [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. [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. [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. [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. doi: 10.1109/81.904893. [18] W. Yu and X. Li, New results on system identification with dynamic neural networks,, IEEE Transactions on Neural Networks, 12 (2001), 412. doi: 10.1109/72.914535. [19] W. Yu, Passivity analysis for dynamic multilayer neuro identifier,, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173.

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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. doi: 10.1016/S0005-1098(96)00180-X. [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. doi: 10.1109/TRO.2008.915438. [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. doi: 10.3934/jimo.2009.5.867. [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. [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. [6] X. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay,, Physical Review E, 68 (2003), 1. doi: 10.1103/PhysRevE.68.016118. [7] X. Y. Lou and B. T. Cui, Passivity analysis of integro-differential neural networks with time-varying delays,, Neurocomputing, 70 (2007), 1071. [8] R. Lozano, B. Brogliato, O. Egeland and B. Maschke, "Systems Analysis and Control: Theory and Applications, Dissipative,", Springer-Verlag, (2000). [9] M. S. Mahmoud and A. Ismail, Passivity and passification of time-delay systems,, Journal of Mathematical Analysis and Applications, 292 (2004), 247. doi: 10.1016/j.jmaa.2003.11.055. [10] J. H. Park, Further results on passivity analysis of delayed cellular neural networks,, Chaos, 34 (2007), 1546. doi: 10.1016/j.chaos.2005.04.124. [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. doi: 10.1016/j.jprocont.2007.07.007. [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. doi: 10.1109/TCSII.2006.886464. [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. doi: 10.1021/ie070599c. [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. [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. [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. [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. doi: 10.1109/81.904893. [18] W. Yu and X. Li, New results on system identification with dynamic neural networks,, IEEE Transactions on Neural Networks, 12 (2001), 412. doi: 10.1109/72.914535. [19] W. Yu, Passivity analysis for dynamic multilayer neuro identifier,, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173.
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