Improved exponential stability criterion for neural networks with time-varying delay

In this paper, the exponential stability for a class of neural networks with time-varying delay is concerned. An improved integral inequality is derived which extends the auxiliary function-based integral inequality. A novel Lyapounov-Krasovskii functional (LKF) with some new integral terms is constructed. Based on the improved integral inequality and reciprocally convex combination approach, a less conservative exponential stability criterion for the neural networks with time-varying delay is obtained. The effectiveness of the proposed method in this paper is illustrated via numerical examples.

[1]  Vladimir E. Bondarenko.  Information processing, memories, and synchronization in chaotic neural network with the time delay , 2005 .

[2]  PooGyeon Park,et al.  Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems , 2015, J. Frankl. Inst..

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

[4]  Jian-an Wang,et al.  Less conservative stability criteria for neural networks with interval time-varying delay based on delay-partitioning approach , 2015, Neurocomputing.

[5]  Xiangjun Xie,et al.  Improved delay-dependent stability analysis for neural networks with time-varying delays. , 2014, ISA transactions.

[6]  Ju H. Park,et al.  A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays , 2013, Neurocomputing.

[7]  Leon O. Chua,et al.  Cellular Neural Networks and Visual Computing: Foundations and Applications , 2002 .

[8]  Leon O. Chua,et al.  Cellular Neural Networks and Visual Computing , 2002 .

[9]  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.

[10]  Min Wu,et al.  Delay-Dependent Stability Criteria for Generalized Neural Networks With Two Delay Components , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Min Wu,et al.  Further results on exponential stability of neural networks with time-varying delay , 2015, Appl. Math. Comput..

[12]  Zhenyuan Guo,et al.  Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations , 2014 .

[13]  Min Wu,et al.  Novel stability criteria for recurrent neural networks with time-varying delay , 2014, Neurocomputing.

[14]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

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

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

[17]  Qing-Long Han,et al.  Global Asymptotic Stability for a Class of Generalized Neural Networks With Interval Time-Varying Delays , 2011, IEEE Trans. Neural Networks.

[18]  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).

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

[20]  Huijun Gao,et al.  New Delay-Dependent Exponential Stability for Neural Networks With Time Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Min Wu,et al.  LMI-based stability criteria for neural networks with multiple time-varying delays , 2005 .

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

[23]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

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

[25]  X. Guan,et al.  New results on stability analysis of neural networks with time-varying delays , 2006 .

[26]  Huaguang Zhang,et al.  New Delay-Dependent Global Exponential Stability Criterion for Cellular-Type Neural Networks With Time-Varying Delays , 2009, IEEE Trans. Circuits Syst. II Express Briefs.

[27]  Ju H. Park,et al.  On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov-Krasovskii functional , 2014, Commun. Nonlinear Sci. Numer. Simul..

[28]  Ju H. Park,et al.  New approaches on stability criteria for neural networks with interval time-varying delays , 2012, Appl. Math. Comput..

[29]  Xiaodi Li,et al.  Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations , 2011, J. Frankl. Inst..

[30]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[31]  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.

[32]  Jian Yu,et al.  Triple-integral method for the stability analysis of delayed neural networks , 2013, Neurocomputing.

[33]  Guang-Hong Yang,et al.  New Delay-Dependent Stability Results for Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[34]  Wei Xing Zheng,et al.  Improved Delay-Dependent Asymptotic Stability Criteria for Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[35]  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.