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

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.

[1]  Jun Wang,et al.  Attractivity Analysis of Memristor-Based Cellular Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[2]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[3]  Lihua Xie,et al.  Passivity analysis for uncertain signal processing systems , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[4]  Igor N. Aizenberg,et al.  Complex-Valued Neural Networks with Multi-Valued Neurons , 2011, Studies in Computational Intelligence.

[5]  Xiaodi Li,et al.  Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays , 2015, Inf. Sci..

[6]  Zhenjiang Zhao,et al.  Global μ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays , 2014 .

[7]  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.

[8]  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.

[9]  Pagavathigounder Balasubramaniam,et al.  An LMI approach for global robust dissipativity analysis of T-S fuzzy neural networks with interval time-varying delays , 2012, Expert Syst. Appl..

[10]  Guodong Zhang,et al.  New Algebraic Criteria for Synchronization Stability of Chaotic Memristive Neural Networks With Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[11]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[12]  Tae H. Lee,et al.  Stochastic sampled-data control for state estimation of time-varying delayed neural networks , 2013, Neural Networks.

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

[14]  Zhigang Zeng,et al.  Anti-synchronization control of a class of memristive recurrent neural networks , 2013, Commun. Nonlinear Sci. Numer. Simul..

[15]  Jinde Cao,et al.  Global dissipativity analysis on uncertain neural networks with mixed time-varying delays. , 2008, Chaos.

[16]  Akira Hirose,et al.  Complex-Valued Neural Networks: Theories and Applications , 2003 .

[17]  Jun Wang,et al.  Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.

[18]  Jinde Cao,et al.  Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays , 2014, Nonlinear Dynamics.

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

[20]  Hamid Reza Karimi,et al.  New Results on Passivity Analysis for Uncertain Neural Networks with Time-Varying Delay , 2014 .

[21]  Huaicheng Yan,et al.  Stability and dissipative analysis for a class of stochastic system with time-delay , 2010, J. Frankl. Inst..

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

[23]  Xiaohong Wang,et al.  Global Robust Exponential Dissipativity for Interval Recurrent Neural Networks with Infinity Distributed Delays , 2013 .

[24]  Madan M. Gupta,et al.  Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory , 2003 .

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

[26]  Yan Sun,et al.  Dissipativity analysis of neural networks with time-varying delays , 2008, Int. J. Autom. Comput..

[27]  Lihua Xie,et al.  Passivity analysis and passification for uncertain signal processing systems , 1998, IEEE Trans. Signal Process..

[28]  Ju H. Park,et al.  Extended Dissipative Analysis for Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

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

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

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

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

[33]  Qiankun Song,et al.  Global -Stability of Complex-Valued Neural Networks with Unbounded Time-Varying Delays , 2014 .

[34]  Hao Shen,et al.  Robust extended dissipative control for sampled-data Markov jump systems , 2014, Int. J. Control.

[35]  Jun Wang,et al.  Global dissipativity of continuous-time recurrent neural networks with time delay. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  T Soddemann,et al.  散逸粒子動力学:平衡および非平衡分子動力学シミュレーションのための有用なサーモスタット(原標題は英語) , 2003 .

[37]  R. Rakkiyappan,et al.  Passivity Analysis of Memristor-Based Complex-Valued Neural Networks with Time-Varying Delays , 2014, Neural Processing Letters.

[38]  Jacek M. Zurada,et al.  A class of discrete-time recurrent neural networks with multivalued neurons , 2009, IJCNN.

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

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

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

[42]  Jun Wang,et al.  Passivity and Passification of Memristor-Based Recurrent Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[43]  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.

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

[45]  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).

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

[47]  Jinde Cao,et al.  Nonsmooth finite-time stabilization of neural networks with discontinuous activations , 2014, Neural Networks.

[48]  J. Hale.  Asymptotic Behavior of Dissipative Systems , 1988 .

[49]  Zhigang Zeng,et al.  Exponential passivity of memristive neural networks with time delays , 2014, Neural Networks.