Novel stability criteria for recurrent neural networks with time-varying delay

Abstract This paper is concerned with the problem of stability analysis of recurrent neural networks with time-varying delay. An augmented Lyapunov–Krasovskii functional containing a triple integral term and considering more information of activation functions is constructed. Then, Wirtinger-based inequality and two zero-value free-weighting matrix equations are used to deal with the derivative of the Lyapunov–Krasovskii functional. Those treatments lead to less conservatism. A numerical example is given to verify the effectiveness and benefit of the proposed criteria.

[1]  Xiaodong Liu,et al.  Stability analysis for neural networks with time-varying delay , 2008, 2008 47th IEEE Conference on Decision and Control.

[2]  Wei Xing Zheng,et al.  Delay-Slope-Dependent Stability Results of Recurrent Neural Networks , 2011, IEEE Transactions on Neural Networks.

[3]  Yijing Wang,et al.  A New Method for Stability Analysis of Recurrent Neural Networks With Interval Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[4]  Jin-Hua She,et al.  Delay-dependent exponential stability of delayed neural networks with time-varying delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Guoping Liu,et al.  Improved delay-range-dependent stability criteria for linear systems with time-varying delays , 2010, Autom..

[6]  James Lam,et al.  Stability and Dissipativity Analysis of Static Neural Networks With Time Delay , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[8]  Xinghuo Yu,et al.  A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  Ting Wang,et al.  Combined Convex Technique on Delay-Dependent Stability for Delayed Neural Networks , 2013, IEEE Transactions on Neural Networks and Learning Systems.

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

[11]  Jie Chen,et al.  New stability criteria for recurrent neural networks with interval time-varying delay , 2013, Neurocomputing.

[12]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[13]  Ju H. Park,et al.  Stability for Neural Networks With Time-Varying Delays via Some New Approaches , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Qing-Long Han,et al.  New Lyapunov-Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks , 2009, IEEE Trans. Neural Networks.

[15]  Shen-Ping Xiao,et al.  New Globally Asymptotic Stability Criteria for Delayed Cellular Neural Networks , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Fang Liu,et al.  Exponential Stability Analysis for Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Ju H. Park,et al.  Analysis on delay-dependent stability for neural networks with time-varying delays , 2013, Neurocomputing.

[18]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[19]  Xin-Ping Guan,et al.  New Exponential Stability Criteria for Neural Networks With Time-Varying Delay , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Bin Jiang,et al.  LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures , 2011, IEEE Transactions on Neural Networks.

[21]  Geng Ji Adaptive neural network dynamic surface control for perturbed nonlinear time-delay systems , 2012, Int. J. Autom. Comput..

[22]  Zidong Wang,et al.  Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays , 2013, IEEE Transactions on Cybernetics.

[23]  Zhigang Zeng,et al.  Multistability of Recurrent Neural Networks With Time-varying Delays and the Piecewise Linear Activation Function , 2010, IEEE Transactions on Neural Networks.

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

[25]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Complex Networks With Uncertain Inner Coupling and Incomplete Measurements , 2013, IEEE Transactions on Neural Networks and Learning Systems.

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

[27]  Huaguang Zhang,et al.  An LMI Approach to Stability Analysis of Reaction–Diffusion Cohen–Grossberg Neural Networks Concerning Dirichlet Boundary Conditions and Distributed Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Huaguang Zhang,et al.  Novel Exponential Stability Criteria of High-Order Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).