Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks

In this paper, impulsive synchronization of stochastic memristor-based recurrent neural networks with time delay is studied. One can find that the memristive connection weights have a certain relationship with the stability of the system. Based on the drive-response concept, the stochastic differential inclusions theory and the Lyapunov functional method with the impulsive delay differential inequality technique was established to guarantee the impulsive synchronization of memristor-based recurrent neural networks with stochastic effects. The obtained sufficient conditions can be checked easily by Linear Matrix Inequalities (LMI) Control Toolbox in MATLAB. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

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

[2]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[3]  Shiping Wen,et al.  Synchronization control of stochastic memristor-based neural networks with mixed delays , 2015, Neurocomputing.

[4]  Shengyuan Xu,et al.  Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays , 2012, J. Frankl. Inst..

[5]  Jun Li,et al.  Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays , 2014, Neurocomputing.

[6]  Shiji Song,et al.  Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method , 2014, Commun. Nonlinear Sci. Numer. Simul..

[7]  Martin Bohner,et al.  An impulsive delay differential inequality and applications , 2012, Comput. Math. Appl..

[8]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[9]  Jitao Sun,et al.  Robust synchronization of coupled delayed neural networks under general impulsive control , 2009 .

[10]  Jinde Cao,et al.  Robust State Estimation for Uncertain Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[11]  Zhigang Zeng,et al.  Exponential Stabilization of Memristive Neural Networks With Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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

[13]  Jinde Cao,et al.  Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control , 2014, Neurocomputing.

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

[15]  Martin Bohner,et al.  Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback , 2010, Math. Comput. Model..

[16]  Minghui Jiang,et al.  New results on exponential synchronization of memristor-based chaotic neural networks , 2015, Neurocomputing.

[17]  Jinde Cao,et al.  Master-slave synchronization of chaotic systems with a modified impulsive controller , 2013 .

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

[19]  Jinde Cao,et al.  Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays , 2014, Cognitive Neurodynamics.

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

[21]  Xinsong Yang,et al.  Synchronization of TS fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects , 2014, Fuzzy Sets Syst..

[22]  Lixiang Li,et al.  Synchronization control of memristor-based recurrent neural networks with perturbations , 2014, Neural Networks.

[23]  Guodong Zhang,et al.  Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control , 2014, Neural Networks.

[24]  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.

[25]  Zhigang Zeng,et al.  Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks , 2014, Neural Networks.

[26]  Chao Ma,et al.  A Stochastic Sampling Consensus Protocol of Networked Euler–Lagrange Systems With Application to Two-Link Manipulator , 2015, IEEE Transactions on Industrial Informatics.

[27]  Yi Shen,et al.  Exponential synchronization of coupled memristive neural networks with time delays , 2013, Neural Computing and Applications.

[28]  Jinde Cao,et al.  Periodicity and synchronization of coupled memristive neural networks with supremums , 2015, Neurocomputing.

[29]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

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

[31]  Mohammad Haeri,et al.  Modified impulsive synchronization of hyperchaotic systems , 2010 .

[32]  Ju H. Park,et al.  Reliable mixed passive and ℋ∞ filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures , 2015 .