Extended dissipative conditions for memristive neural networks with multiple time delays

This paper addresses the problem of extended dissipative conditions for memristive neural networks with multiple time delays. The multiple time delays contain discrete, distributed and leakage time-varying delays. Based on both nonsmooth analysis and Lyapunov method, the extended dissipative conditions are obtained by mainly applying differential inclusions, set-valued maps and some new integral inequalities. The extended dissipative conditions can be applied in judging l2−l∞ performance, H∞ action, passive behavior and dissipative dynamics in a unified framework. Finally, a numerical example is provided to demonstrate the effectiveness and less conservatism of the proposed criteria.

[1]  Fernando Corinto,et al.  Nonlinear Dynamics of Memristor Oscillators , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Ju H. Park,et al.  Mean square exponential synchronization for impulsive coupled neural networks with time-varying delays and stochastic disturbances , 2016, Complex..

[3]  Jinde Cao,et al.  Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances , 2017, Appl. Math. Comput..

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

[5]  Wei Yang Lu,et al.  Nanoscale memristor device as synapse in neuromorphic systems. , 2010, Nano letters.

[6]  Zhigang Zeng,et al.  Lagrange Stability of Memristive Neural Networks With Discrete and Distributed Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Hao Shen,et al.  Extended dissipativity-based synchronization of uncertain chaotic neural networks with actuator failures , 2015, J. Frankl. Inst..

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

[9]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[10]  K. Gopalsamy.  Leakage delays in BAM , 2007 .

[11]  Jinde Cao,et al.  Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays , 2015, Neural Networks.

[12]  Xinzhi Liu,et al.  Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation. , 2017, ISA transactions.

[13]  Zhigang Zeng,et al.  Circuit design and exponential stabilization of memristive neural networks , 2015, Neural Networks.

[14]  Zhigang Zeng,et al.  Exponential Adaptive Lag Synchronization of Memristive Neural Networks via Fuzzy Method and Applications in Pseudorandom Number Generators , 2014, IEEE Transactions on Fuzzy Systems.

[15]  Xinzhi Liu,et al.  Novel integral inequality approach on master–slave synchronization of chaotic delayed Lur’e systems with sampled-data feedback control , 2016 .

[16]  Zhigang Zeng,et al.  Exponential synchronization of memristor-based recurrent neural networks with time delays , 2011, Neurocomputing.

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

[18]  Ju H. Park,et al.  Non-fragile H∞ synchronization of memristor-based neural networks using passivity theory , 2016, Neural Networks.

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

[20]  Ju H. Park,et al.  Further Results on Stabilization of Chaotic Systems Based on Fuzzy Memory Sampled-Data Control , 2018, IEEE Transactions on Fuzzy Systems.

[21]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

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

[23]  Zhigang Zeng,et al.  Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.

[24]  Lihong Huang,et al.  Periodicity and dissipativity for memristor-based mixed time-varying delayed neural networks via differential inclusions , 2014, Neural Networks.

[25]  Ju H. Park,et al.  Stability and dissipativity analysis of static neural networks with interval time-varying delay , 2015, J. Frankl. Inst..

[26]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Hao Shen,et al.  Robust passivity analysis of neural networks with discrete and distributed delays , 2015, Neurocomputing.

[28]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[29]  Shouming Zhong,et al.  New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays. , 2015, ISA transactions.

[30]  Xinzhi Liu,et al.  On designing stochastic sampled-data controller for master-slave synchronization of chaotic Lur'e system via a novel integral inequality , 2016, Commun. Nonlinear Sci. Numer. Simul..

[31]  Xinzhi Liu,et al.  Some novel approaches on state estimation of delayed neural networks , 2016, Inf. Sci..

[32]  Z. Zeng,et al.  Passivity and passification of stochastic impulsive memristor‐based piecewise linear system with mixed delays , 2015 .

[33]  Jinde Cao,et al.  Pth Moment Exponential Stochastic Synchronization of Coupled Memristor-based Neural Networks with Mixed Delays via Delayed Impulsive Control , 2015, Neural Networks.

[34]  Min Wu,et al.  Dissipativity analysis of neural networks with time-varying delays , 2015, Neurocomputing.

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

[36]  Ju H. Park,et al.  Reliable stabilization for memristor-based recurrent neural networks with time-varying delays , 2015, Neurocomputing.

[37]  Ju H. Park,et al.  State estimation of memristor-based recurrent neural networks with time-varying delays based on passivity theory , 2014, Complex..

[38]  Wei Xing Zheng,et al.  On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[39]  Shouming Zhong,et al.  Extended dissipative state estimation for memristive neural networks with time-varying delay. , 2016, ISA transactions.

[40]  Jinde Cao,et al.  New synchronization criteria for memristor-based networks: Adaptive control and feedback control schemes , 2015, Neural Networks.

[41]  Jinde Cao,et al.  Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays , 2015, Appl. Math. Comput..

[42]  Jin-Hua She,et al.  New results on stability analysis for systems with discrete distributed delay , 2015, Autom..

[43]  Rathinasamy Sakthivel,et al.  Combined H∞ and passivity state estimation of memristive neural networks with random gain fluctuations , 2015, Neurocomputing.

[44]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[45]  Shengyuan Xu,et al.  Relaxed passivity conditions for neural networks with time-varying delays , 2014, Neurocomputing.

[46]  Ju H. Park,et al.  Impulsive Effects on Quasi-Synchronization of Neural Networks With Parameter Mismatches and Time-Varying Delay , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[47]  Ju H. Park,et al.  Stability of time-delay systems via Wirtinger-based double integral inequality , 2015, Autom..