New algebraic conditions for ISS of memristive neural networks with variable delays

In this paper, a general class of memristive neural networks with variable delays is studied. By utilizing control theory and nonsmoooth analysis, two sufficient criteria ensuring input-to-state stability of memristive neural networks with variable delays are firstly obtained which are novel and more practical than the previous works in the literature. Finally, a numerical example is given to demonstrate the effectiveness of our results.

[1]  David J. Hill,et al.  Lyapunov formulation of ISS cyclic-small-gain in continuous-time dynamical networks , 2011, Autom..

[2]  Leon O. Chua,et al.  Neural Synaptic Weighting With a Pulse-Based Memristor Circuit , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Massimiliano Di Ventra,et al.  Experimental demonstration of associative memory with memristive neural networks , 2009, Neural Networks.

[4]  Eduardo Sontag Input to State Stability: Basic Concepts and Results , 2008 .

[5]  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).

[6]  Shengyuan Xu,et al.  Improved global robust asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  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.

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

[9]  Eduardo Sontag,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999, at - Automatisierungstechnik.

[10]  Lihua Xie,et al.  Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay , 2007, IEEE Transactions on Automatic Control.

[11]  Mark W. Spong,et al.  ROBUST STABILIZATION FOR A CLASS OF NONLINEAR SYSTEMS. , 1986 .

[12]  Daniel E. Quevedo,et al.  Input-to-State Stability of Packetized Predictive Control Over Unreliable Networks Affected by Packet-Dropouts , 2011, IEEE Transactions on Automatic Control.

[13]  Eduardo Sontag Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[14]  Zhigang Zeng,et al.  Synchronization control of a class of memristor-based recurrent neural networks , 2012, Inf. Sci..

[15]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

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

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

[18]  Song Zhu,et al.  Further results on robustness analysis of global exponential stability of recurrent neural networks with time delays and random disturbances , 2014, Neural Networks.

[19]  Zidong Wang,et al.  Neural networks with discrete and distributed time-varying delays: A general stability analysis , 2008 .

[20]  Thomas Parisini,et al.  Networked Predictive Control of Uncertain Constrained Nonlinear Systems: Recursive Feasibility and Input-to-State Stability Analysis , 2011, IEEE Transactions on Automatic Control.

[21]  Song Zhu,et al.  Robustness analysis for connection weight matrices of global exponential stability of stochastic recurrent neural networks , 2013, Neural Networks.

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

[23]  Eduardo Sontag,et al.  New characterizations of input-to-state stability , 1996, IEEE Trans. Autom. Control..

[24]  Zhigang Zeng,et al.  Input-to-State Stability of Memristive Neural System with Time Delays , 2014, Circuits Syst. Signal Process..

[25]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[26]  Sabri Arik,et al.  New Criteria for Global Robust Stability of Delayed Neural Networks With Norm-Bounded Uncertainties , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[28]  Jinling Liang,et al.  Robust stabilisation for a class of stochastic two-dimensional non-linear systems with time-varying delays , 2013 .

[29]  Emilia Fridman,et al.  On input-to-state stability of systems with time-delay: A matrix inequalities approach , 2008, Autom..

[30]  Zhigang Zeng,et al.  H∞ Filtering for Neutral Systems With Mixed Delays and Multiplicative Noises , 2012, IEEE Trans. Circuits Syst. II Express Briefs.

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

[32]  Song Zhu,et al.  Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays , 2013, Neural Computing and Applications.

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

[34]  Zidong Wang,et al.  Global Synchronization in an Array of Discrete-Time Neural Networks with Nonlinear Coupling and Time-Varying Delays , 2009, Int. J. Neural Syst..

[35]  Chuandong Li,et al.  Delay-interval-dependent stability of recurrent neural networks with time-varying delay , 2009, Neurocomputing.

[36]  Zidong Wang,et al.  On global exponential stability of generalized stochastic neural networks with mixed time-delays , 2006, Neurocomputing.

[37]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[38]  Zhigang Zeng,et al.  $H_{\infty}$ Filtering for Neutral Systems With Mixed Delays and Multiplicative Noises , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[39]  Mohammad Javad Sharifi,et al.  General SPICE Models for Memristor and Application to Circuit Simulation of Memristor-Based Synapses and Memory Cells , 2010, J. Circuits Syst. Comput..