Improved Stability Criterion for Recurrent Neural Networks With Time-Varying Delays

In this brief, the problem of delay-dependent stability of recurrent neural networks with time-varying delays is studied. A newly augmented Lyapunov–Krasovskii functional (LKF) that considers the information of the nonzero lower bound of time-varying delays is developed. Moreover, the information of the delayed state terms is not considered as elements of augmented vectors when constructing the LKF. An improved stability criterion with the framework of linear matrix inequalities is derived by employing the integral inequality and reciprocally convex combination. With the comparison to the existing ones, the developed stability criterion for neural networks has less conservatism and complexity. Finally, two widely used numerical examples are given to show the effectiveness and superiority of the obtained stability criterion.

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

[2]  Ju H. Park,et al.  New approach to stability criteria for generalized neural networks with interval time-varying delays , 2015, Neurocomputing.

[3]  Xin-Ping Guan,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Yong He,et al.  Stability analysis of neural networks with time-varying delay: Enhanced stability criteria and conservatism comparisons , 2018, Commun. Nonlinear Sci. Numer. Simul..

[5]  Ju H. Park,et al.  An improved stability criterion for generalized neural networks with additive time-varying delays , 2016, Neurocomputing.

[6]  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.

[7]  Min Wu,et al.  Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach , 2017, Appl. Math. Comput..

[8]  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.

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

[10]  Shen-Ping Xiao,et al.  Stability analysis of generalized neural networks with time-varying delays via a new integral inequality , 2015, Neurocomputing.

[11]  Georgi M. Dimirovski,et al.  New delay-dependent stability criteria for recurrent neural networks with time-varying delays , 2008, Neurocomputing.

[12]  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..

[13]  Qing-Long Han,et al.  Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach , 2014, Neural Networks.

[14]  Huanhuan Li,et al.  New stability results for delayed neural networks , 2017, Appl. Math. Comput..

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

[16]  Wei Xing Zheng,et al.  On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Ju H. Park,et al.  New and improved results on stability of static neural networks with interval time-varying delays , 2014, Appl. Math. Comput..

[18]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Huaguang Zhang,et al.  Stability Criteria for Recurrent Neural Networks With Time-Varying Delay Based on Secondary Delay Partitioning Method , 2015, IEEE Transactions on Neural Networks and Learning Systems.

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

[21]  Huaguang Zhang,et al.  Stability Analysis of Neural Networks With Two Delay Components Based on Dynamic Delay Interval Method , 2017, IEEE Transactions on Neural Networks and Learning Systems.

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

[23]  Huaguang Zhang,et al.  Stability of Recurrent Neural Networks With Time-Varying Delay via Flexible Terminal Method , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[25]  Raman Manivannan,et al.  An improved delay-partitioning approach to stability criteria for generalized neural networks with interval time-varying delays , 2017, Neural Computing and Applications.

[26]  Shouming Zhong,et al.  Delay-partitioning approach to stability analysis of generalized neural networks with time-varying delay via new integral inequality , 2016, Neurocomputing.

[27]  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.

[28]  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).