Journal of Guangdong University of Technology ›› 2017, Vol. 34 ›› Issue (01): 78-83,89.doi: 10.12052/gdutxb.150151

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Passivity Analysis for Uncertain Neural Networks with Time-Varying Delay

Peng Shi-you, Peng Shi-guo   

  1. School of Automation, Guangdong University of Technology, Guangzhou 510006, China
  • Received:2015-12-28 Online:2017-01-09 Published:2017-01-09

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Abstract:

The passivity of neural networks of neural network systems is studied. Based on the passive network theory, it the less conservative conditions of the neural network can be obtained. Additionally, the robust passivity of the parameters uncertainties' neural networks with time-delay is analyzed. According to theories and approaches of Lyapunov stability, Jensen integral inequality, Schur complement lemma and free weighting matrices, the research shows that the less conservative passive condition of the neural network can be obtained from constructing a new Lyapunov-Krasovskii functional and simplifying the quadratic terms of the Lyapunov-Krasovskii functional's inverse. Meanwhile, the passivity condition is obtained not requiring all the symmetric involved in the employed quadratic Lyapunov-Krasovskii functional matrices to be positive definite. The results show that the method is effective.

Key words: neural networks, Lyapunov-Krasovskii functional, time delay

CLC Number: 

  • TP273

[1] GUPTA M, JIN L, Homma N. Static and Dynamic Neural Networks:From Fundamentals to Advanced Theory[M]. New York:Wiley-IEEE Press, 2003.
[2] 郑胜林, 彭明明, 潘保昌. 一种基于Hough变换的神经网络字符识别方法[J]. 广东工业大学学报, 2003, 20(4):73-77. ZHENG S L, PENG M M, PAN B C. A method for characters recognition based on the hough transform and neural network[J]. Journal of Guangdong University of Technology, 2003, 20(4):73-77.
[3] ENSARI T, ARIK S. Global stability of a class of neural networks with time-varying delay[J]. IEEE Transactions on Circuits Systems II:Analog and Digital Signal Processing, 2005, 52(2):126-130.
[4] KWON O M, PARK J H, Lee S M. On robust stability for uncertain cellular neural networks with interval time varying delays[J]. IET Control Theory & Applications, 2008, 2(7):625-634.
[5] KWON O M, PARK J H. Delay dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays[J]. Journal of the Franklin Institute, 2008, 345(7):766-778.
[6] ZHU Q X, CAO J D. Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays[J]. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(3):467-479.
[7] ZHANG C K, HE Y, LI J, et al. Delay-dependent stability criteria for generalized neural networks with two delay components[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(7):1263-1276.
[8] HILL D, MOYLAN P. The stability of nonlinear dissipative systems[J]. IEEE Transactions on Automatic Control, 1976, 21(5):708-711.
[9] LOZANO R, BROGLIATO B, EGELAND O, et al. Dissipative Systems Analysis and Control:Theory and Applications[M]. London, UK.:Springer, 2007.
[10] XIE L H, FU M Y, LI H Z. Passivity analysis and passification for uncertain signal processing systems[J]. IEEE Transactions on Signal Process, 1998, 46(9):2394-2403.
[11] WU C W. Synchronization in arrays of coupled nonlinear systems:passivity circle criterion and observer design[J]. IEEE Transactions on Circuits and Systems. I:Fundamental Theory and Applications, 2001, 48(10):1257-1261.
[12] LI C G, LIAO X F. Passivity analysis of neural networks with time delay[J]. IEEE Transactions on Circuits and Systems II:Analog and Digital Signal Processing, 2005, 52(8):471-475.
[13] LOU X Y, CUI B T. Passivity analysis of integro-differential neural networks with time-varying delays[J]. Neurocomputing, 2007, 70(4-6):1071-1078.
[14] ZHU J, LENG Q K, ZHANG Q L. Delay-dependent passivity criterion for hopfield neural networks[C]. 2010 Chinese Control and Decision Conference, Xuzhou, China, 2010:1267-1272.
[15] ZENG H B, HE Y, WU M, et al. Passivity analysis for neural with a time-varying delay[J]. Neurocomputing, 2011, 74(5):730-734.
[16] ZENG H B, XIAO S P, ZHANG C F, et al. Further results on passivity analysis of neural networks with time-varying delay[C], 26th Chinese Control and Decision Conference (CCDC), Changsha, China, 2014:161-165.
[17] ZHANG B Y, XU S Y, LAM J. Relaxed passivity condition for neural networks with time-varying delays[J]. Neurocomputing, 2014, 142(1):299-306.
[18] WANG Z D, LIU Y R, LIU X H. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays[J]. Neural Networks, 2006, 19(5):667-675.
[19] GU K. An integral inequality in the stability problem of time-delay systems[C]. Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, 3(3):2805-2810.
[20] PARK P G, KO J W, JEONG C. Reciprocally convex approach to stability of systems with time-varying delays[J]. Automatica, 2011, 47(1):235-238.
[21] BOYD S, GHAOHUI L E, FERON E, et al. Linear matrix inequalities in system and control theory[M]. Philadelp-hiaz:SIAM, 1994.
[22] PETERSEN I R, HOLLOT C V. A Riccati equation approach to the stabilization of uncertain linear systems[J]. Automatica, 1986, 22(4):397-411.
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