Global exponential stability of uncertain neural networks with discontinuous Lurie-type activation and mixed delays

This paper deals with the problem of the global exponential stability of a class of uncertain neural networks with discontinuous Lurie-type activation and mixed delays. By establishing a new sufficient condition, we first prove the existence of the equilibrium point by using the Leray-Schauder alternative theorem. Then, by employing a new Lyapunov functional, we obtain the global exponential stability of the equilibrium point of the uncertain neural network. In the end, some comparisons and numerical examples are given to show the improvement of the conclusions in this paper.

[1]  Lihong Huang,et al.  Finite time stability of periodic solution for Hopfield neural networks with discontinuous activations , 2013, Neurocomputing.

[2]  Lihong Huang,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with mixed time delays and discontinuous activations , 2013, Neurocomputing.

[3]  Zhengqiu Zhang,et al.  Novel LMI-based condition on global asymptotic stability for BAM neural networks with reaction-diffusion terms and distributed delays , 2014, Neurocomputing.

[4]  Sitian Qin,et al.  A new one-layer recurrent neural network for nonsmooth pseudoconvex optimization , 2013, Neurocomputing.

[5]  Jun Wang,et al.  A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits , 2003, IEEE Trans. Neural Networks.

[6]  Sitian Qin,et al.  Convergence analysis for second-order interval Cohen-Grossberg neural networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[7]  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.

[8]  Sabri Arik,et al.  Robust stability analysis of a class of neural networks with discrete time delays , 2012, Neural Networks.

[9]  Jinde Cao,et al.  A Novel Recurrent Neural Network with Finite-Time Convergence for Linear Programming , 2010, Neural Computation.

[10]  Shu-Cherng Fang,et al.  A neural network model with bounded-weights for pattern classification , 2004, Comput. Oper. Res..

[11]  Zhigang Zeng,et al.  Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays , 2012, Neurocomputing.

[12]  Z. Zeng,et al.  Adaptive synchronization of memristor-based Chuaʼs circuits , 2012 .

[13]  Lihong Huang,et al.  On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions , 2012, Neural Networks.

[14]  Lihong Huang,et al.  Global exponential stability of fuzzy BAM neural networks with distributed delays and time-varying delays in the leakage terms , 2012, Neural Computing and Applications.

[15]  Zhigang Zeng,et al.  Multistability of Neural Networks With Time-Varying Delays and Concave-Convex Characteristics , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[16]  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.

[17]  Lian Duan,et al.  Existence and stability of periodic solution for mixed time-varying delayed neural networks with discontinuous activations , 2014, Neurocomputing.

[18]  Sabri Arik,et al.  A new robust stability criterion for dynamical neural networks with multiple time delays , 2013, Neurocomputing.

[19]  Jun Wang,et al.  A systematic method for analyzing robust stability of interval neural networks with time-delays based on stability criteria , 2014, Neural Networks.

[20]  Sitian Qin,et al.  Global Exponential Stability and Global Convergence in Finite Time of Neural Networks with Discontinuous Activations , 2009, Neural Processing Letters.

[21]  Xing-Bao Gao,et al.  A novel neural network for nonlinear convex programming , 2004, IEEE Trans. Neural Networks.

[22]  Lihong Huang,et al.  Dynamical behaviors for discontinuous and delayed neural networks in the framework of Filippov differential inclusions , 2013, Neural Networks.

[23]  Sabri Arik,et al.  Equilibrium and stability analysis of delayed neural networks under parameter uncertainties , 2012, Appl. Math. Comput..

[24]  Qingshan Liu,et al.  Finite-Time Convergent Recurrent Neural Network With a Hard-Limiting Activation Function for Constrained Optimization With Piecewise-Linear Objective Functions , 2011, IEEE Transactions on Neural Networks.

[25]  Zhigang Zeng,et al.  Global asymptotic stability of delayed neural networks with discontinuous neuron activations , 2013, Neurocomputing.

[26]  Sabri Arik,et al.  A new condition for robust stability of uncertain neural networks with time delays , 2014, Neurocomputing.

[27]  Sitian Qin,et al.  Global Robust Exponential Stability for Interval Delayed Neural Networks with Possibly Unbounded Activation Functions , 2013, Neural Processing Letters.

[28]  Ting-Zhu Huang,et al.  Some improved criteria for global robust exponential stability of neural networks with time-varying delays , 2010 .

[29]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[30]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[31]  Sitian Qin,et al.  Dynamical behavior of a class of nonsmooth gradient-like systems , 2010, Neurocomputing.

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

[33]  Peng Wang,et al.  Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations , 2013, Inf. Sci..

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

[35]  Sabri Arik,et al.  An improved robust stability result for uncertain neural networks with multiple time delays , 2014, Neural Networks.

[36]  Lihong Huang,et al.  LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations , 2009, Appl. Math. Comput..

[37]  Mustafa Sayli,et al.  Global robust asymptotic stability of variable-time impulsive BAM neural networks , 2014, Neural Networks.

[38]  Yingwei Li,et al.  Global stability analysis in Cohen-Grossberg neural networks with delays and inverse Hölder neuron activation functions , 2010, Inf. Sci..

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

[40]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[41]  Lihong Huang,et al.  Global dynamics of equilibrium point for delayed competitive neural networks with different time scales and discontinuous activations , 2014, Neurocomputing.