Passivity Analysis of Memristor-Based Complex-Valued Neural Networks with Time-Varying Delays

In this paper, the model of memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is established and the problem of passivity analysis for MCVNNs is considered and extensively investigated. The analysis in this paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By employing the appropriate Lyapunov–Krasovskii functional, differential inclusion theory and linear matrix inequality (LMI) approach, some new sufficient conditions for the passivity of the given MCVNNs are obtained in terms of both complex-valued and real-value LMIs, which can be easily solved by using standard numerical algorithms. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

[1]  Y. Pershin,et al.  Spin Memristive Systems: Spin Memory Effects in Semiconductor Spintronics , 2008, 0806.2151.

[2]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays , 2012, Neural Networks.

[3]  James Lam,et al.  New passivity criteria for neural networks with time-varying delay , 2009, Neural Networks.

[4]  Zhaoning Yu,et al.  Nonlinear optical spectroscopy of photonic metamaterials , 2007, 2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science.

[5]  Pagavathigounder Balasubramaniam,et al.  A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay , 2011, Neurocomputing.

[6]  Jinde Cao,et al.  Synchronization of Switched Interval Networks and Applications to Chaotic Neural Networks , 2013 .

[7]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[8]  Zhigang Zeng,et al.  Passivity analysis of memristive neural networks with different memductance functions , 2014, Commun. Nonlinear Sci. Numer. Simul..

[9]  Zhigang Zeng,et al.  Passivity analysis of memristor-based recurrent neural networks with time-varying delays , 2013, J. Frankl. Inst..

[10]  Pagavathigounder Balasubramaniam,et al.  Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays , 2012, Expert Syst. Appl..

[11]  Jinde Cao,et al.  LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay , 2007 .

[12]  Yong He,et al.  Passivity analysis for neural networks with a time-varying delay , 2011, Neurocomputing.

[13]  Jinde Cao,et al.  Passivity analysis for switched generalized neural networks with time-varying delay and uncertain output , 2013, IMA J. Math. Control. Inf..

[14]  Jinde Cao,et al.  Passivity of uncertain neural networks with both leakage delay and time-varying delay , 2012 .

[15]  Prem Kumar Kalra,et al.  On Efficient Learning Machine With Root-Power Mean Neuron in Complex Domain , 2011, IEEE Transactions on Neural Networks.

[16]  Jinde Cao,et al.  Cluster synchronization in an array of hybrid coupled neural networks with delay , 2009, Neural Networks.

[17]  Qiankun Song,et al.  Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales , 2013, Neurocomputing.

[18]  Sabri Arik,et al.  An analysis of exponential stability of delayed neural networks with time varying delays , 2004, Neural Networks.

[19]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[20]  Guodong Zhang,et al.  Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays , 2012, Neurocomputing.

[21]  Lajos Hanzo,et al.  Symmetric Complex-Valued RBF Receiver for Multiple-Antenna-Aided Wireless Systems , 2008, IEEE Transactions on Neural Networks.

[22]  Jun Wang,et al.  Global Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Zhigang Zeng,et al.  Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays , 2012, Neurocomputing.

[24]  Akira Hirose,et al.  Complex-Valued Neural Networks (Studies in Computational Intelligence) , 2006 .

[25]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[26]  S. Arik,et al.  New exponential stability results for delayed neural networks with time varying delays , 2004 .

[27]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[28]  Q. Song,et al.  Boundedness and Stability for Discrete-Time Delayed Neural Network with Complex-Valued Linear Threshold Neurons , 2010 .

[29]  Bo Zhou,et al.  Boundedness and complete stability of complex-valued neural networks with time delay. , 2013, IEEE transactions on neural networks and learning systems.

[30]  Jinde Cao,et al.  Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller , 2013, SIAM J. Control. Optim..

[31]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[32]  Chien-Yu Lu,et al.  A Delay-Dependent Approach to Passivity Analysis for Uncertain Neural Networks with Time-varying Delay , 2008, Neural Processing Letters.

[33]  J. Tour,et al.  Electronics: The fourth element , 2008, Nature.

[34]  John H. Mathews,et al.  Complex analysis for mathematics and engineering , 1995 .

[35]  Song Zhu,et al.  Exponential passivity of neural networks with time-varying delay and uncertainty , 2010 .

[36]  Ju H. Park,et al.  New results on exponential passivity of neural networks with time-varying delays , 2012 .

[37]  L. Chua.  Memristor-The missing circuit element , 1971 .

[38]  J. Tour,et al.  The fourth element , 2008 .

[39]  Xin Wang,et al.  Global exponential stability of a class of memristive neural networks with time-varying delays , 2013, Neural Computing and Applications.

[40]  Chun-Guang Li,et al.  Passivity Analysis of Neural Networks With Time Delay , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[41]  Garimella Rama Murthy,et al.  Global Dynamics of a Class of Complex Valued Neural Networks , 2008, Int. J. Neural Syst..

[42]  Jun Wang,et al.  Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[43]  J. Yang,et al.  Memristive switching mechanism for metal/oxide/metal nanodevices. , 2008, Nature nanotechnology.

[44]  Quan Yin,et al.  Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays , 2013, Inf. Sci..

[45]  Jacek M. Zurada,et al.  Discrete-Time Recurrent Neural Networks With Complex-Valued Linear Threshold Neurons , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[46]  Hai Helen Li,et al.  Spintronic Memristor Through Spin-Torque-Induced Magnetization Motion , 2009, IEEE Electron Device Letters.

[47]  Tianguang Chu,et al.  Exponential stability of neural networks with variable delays via LMI approach , 2006 .

[48]  Akira Hirose,et al.  Complex-Valued Neural Networks , 2006, Studies in Computational Intelligence.

[49]  P. Balasubramaniam,et al.  Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays ☆ , 2010 .

[50]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[51]  Jacek M. Zurada,et al.  Discrete-Time Recurrent Neural Networks With Complex-Valued Linear Threshold Neurons , 2009, IEEE Trans. Circuits Syst. II Express Briefs.

[52]  K. Aihara,et al.  Complex-Valued Multistate Associative Memory With Nonlinear Multilevel Functions for Gray-Level Image Reconstruction , 2009, IEEE Transactions on Neural Networks.