Global dissipativity of memristor-based complex-valued neural networks with time-varying delays

详细信息    查看全文

• 作者：R. Rakkiyappan ; G. Velmurugan ; Xiaodi Li…
• 关键词：Memristor ; Complex ; valued neural networks (CVNNs) ; Dissipativity ; M ; matrix theory ; Time delays ; Linear matrix inequality (LMI)
• 刊名：Neural Computing & Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：27
• 期：3
• 页码：629-649
• 全文大小：835 KB
• 参考文献：1.Gupta MM, Jin L, Homma N (2003) Static and dynamic neural networks: from fundamentals to advanced theory. Wiley, New YorkCrossRef
  2.Xie L, Fu M, Li H (1998) Passivity analysis for uncertain signal processing systems. IEEE Trans Signal Process 49:2394–2403
  3.Liu X, Park Ju H, Jiang N, Cao J (2014) Nonsmooth finite-time stabilization of neural networks with discontinuous activations. Neural Netw 52:25–32CrossRef MATH
  4.Hirose A (2003) Complex-valued neural networks: theories and applications. World Scientific, SingaporeCrossRef MATH
  5.Aizenberg I (2011) Complex-valued neural networks with multi-valued neurons. Springer, New YorkCrossRef MATH
  6.Mathews JH, Howell RW (1997) Complex analysis for mathematics and engineering. Jones and Bartlett, BostonMATH
  7.Lee TH, Park Ju H, Kwon OM, Lee SM (2013) Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw 46:99–108CrossRef MATH
  8.Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23:853–865CrossRef
  9.Zhou B, Song QK (2013) Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans Neural Netw Learn Syst 24:1227–1238MathSciNet CrossRef
  10.Chen X, Song QK (2013) Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing 121:254–264MathSciNet CrossRef
  11.Zhou W, Zurada JM (2009) Discrete-time recurrent neural networks with complex-valued linear threshold neurons. IEEE Trans Circuits Syst II Express Briefs 56:669–673CrossRef
  12.Duan CJ, Song QK (2010) Boundedness and stability for discrete-time delayed neural network with complex-valued linear threshold neurons. Discrete Dyn Nat Soc 2010:368–379MathSciNet CrossRef MATH
  13.Zhou W, Zurada JM (2009) A class of discrete time recurrent neural networks with multivalued neurons. Neurocomputing 72:3782–3788CrossRef
  14.Chen X, Song Q, Liu X, Zhao Z (2014) Global μ-stability of complex-valued neural networks with unbounded time-varying delays. Abstr Appl Anal Article ID: 263847
  15.Chen X, Song Q, Liu Y, Zhao Z (2014) Global μ-stability of impulsive complex-valued neural networks with leakage delay and mixed delays. Abstr Appl Anal 2014 Article ID: 397532
  16.Chua LO (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18:507–519CrossRef
  17.Strukov DB, Snider GS, Stewart GR, Williams RS (2008) The missing memristor found. Nature 453:80–83CrossRef
  18.Tour JM, He T (2008) The fourth element. Nature 453:42–43CrossRef
  19.Hu J, Wang J (2010) Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays. In: 2010 international joint conference on neural networks, IJCNN 2010, Barcelona, Spain, pp 1–8
  20.Wu A, Zeng Z (2012) Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays. Neural Netw 36:1–10CrossRef MATH
  21.Wu A, Zeng Z (2013) Anti-synchronization control of a class of memristive recurrent neural networks. Commun Nonlinear Sci Numer Simul 18:373–385MathSciNet CrossRef MATH
  22.Zhang G, Shen Y (2013) New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 24:1701–1707CrossRef
  23.Guo Z, Wang J, Yan Z (2014) Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25:704–717CrossRef
  24.Wu A, Zeng Z (2014) Exponential passivity of memristive neural networks with time delays. Neural Netw 49:11–18CrossRef MATH
  25.Wen S, Zeng Z, Huang T, Chen Y (2013) Passivity analysis of memristor-based recurrent neural networks with time-varying delays. J Frankl Inst 350:2354–2370MathSciNet CrossRef MATH
  26.Wu A, Zeng Z (2014) Passivity analysis of memristive neural networks with different memductance functions. Commun Nonlinear Sci Numer Simul 19:274–285MathSciNet CrossRef
  27.Willems J (1972) Dissipative dynamical systems part I: general theory. Arch Ration Mech Anal 45:321–351MathSciNet CrossRef MATH
  28.Hill D, Moylan P (1980) Dissipative dynamical systems: basic input-output and state properties. J Frankl Inst 309:327–357MathSciNet CrossRef MATH
  29.Zhang H, Yan H, Chen Q (2010) Stability and dissipative analysis for a class of stochastic system with time-delay. J Frankl Inst 347:882–893MathSciNet CrossRef MATH
  30.Hale JK (1988) Asymptotic behavior of dissipative systems. Mathematical surveys and monographs, vol 25. American Mathematical Society, Providence, RI, USA
  31.Liao X, Wang J (2003) Global dissipativity of continuous-time recurrent neural networks with time delay. Phys Rev E 68:1–7MathSciNet CrossRef
  32.Song QK, Cao J (2008) Global dissipativity analysis on uncertain neural networks with mixed time-varying delays. Chaos 18:0431261–10MathSciNet
  33.Sun Y, Cui BT (2008) Dissipativity analysis of neural networks with time-varying delays. Int J Autom Comput 05:290–295CrossRef
  34.Muralisankar S, Gobalakrishnan N, Balasubramaniam P (2012) An LMI approach for global robust dissipativity analysis of T-S fuzzy neural networks with interval time-varying delays. Expert Syst Appl 39:3345–3355CrossRef
  35.Shao X, Lu Q, Karimi HR, Zhu J (2014) New results on passivity analysis for uncertain neural networks with time-varying delay. Abstr Appl Anal Article ID: 303575
  36.Wang X, Qi H (2013) Global robust exponential dissipativity for interval recurrent neural networks with infinity distributed delays. Abstr Appl Anal Article ID 585709
  37.Guo Z, Wang J, Yan Z (2013) Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Netw 48:158–172CrossRef MATH
  38.Shen H, Park Ju H, Zhang L, Wu ZG (2014) Robust extended dissipative control for sampled-data Markov jump systems. Int J Control 87:1549–1564MathSciNet CrossRef MATH
  39.Lee TH, Park MJ, Park Ju H, Kwon OM, Lee SM (2014) Extended dissipative analysis for neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25:1936–1941CrossRef
  40.Velmurugan G, Rakkiyappan R, Lakshmanan S Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett. doi:10.​1007/​s11063-014-9371-8
  41.Rakkiyappan R, Velmurugan G, Cao J (2014) Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays. Nonlinear Dyn 78:2823–2836MathSciNet CrossRef MATH
  42.Li X, Rakkiyappan R, Velmurugan G (2015) Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays. Inf Sci 294:645–665MathSciNet CrossRef
  43.Filippov AF (1988) Differential equations with discontinuous right-hand sides. Kluwer, DordrechtCrossRef MATH
  44.Boyd B, Ghoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRef
  
• 作者单位：R. Rakkiyappan (1)
  G. Velmurugan (1)
  Xiaodi Li (2)
  Donal O’Regan (3)
  
  1. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, Tamil Nadu, India
  2. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, Shandong, People’s Republic of China
  3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
  
• 刊物类别：Computer Science
• 刊物主题：Simulation and Modeling
  
• 出版者：Springer London
• ISSN：1433-3058

文摘

Memristor is the new model two-terminal nonlinear circuit device in electronic circuit theory. This paper deals with the problem of global dissipativity and global exponential dissipativity for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays. Sufficient global dissipativity conditions are derived from the theory of M-matrix analysis, and the globally attractive set as well as the positive invariant set is established. By constructing Lyapunov–Krasovskii functionals and using a linear matrix inequality technique, some new sufficient conditions on global dissipativity and global exponential dissipativity of MCVNNs are derived. Finally, two numerical examples are presented to demonstrate the effectiveness of our proposed theoretical results.