Further improved stability results for generalized neural networks with time-varying delays

Abstract This paper is concerned with a new Lyapunov–Krasovskii functional (LKF) approach to delay-dependent stability for generalized neural networks with time-varying delays (DNN). A new LKF is constructed by employing more information of the DNN. The state, the activation function and their ramifications are introduced, and more cross terms of the activation function and their ramifications are included in the LKF. Moreover, the new LKF also makes best of the characteristic of the activation function. On the other hand, when estimating the derivative of the LKF, we take advantages of some equations and inequalities that reveal the relationship among the state, the activation function and their ramifications, employ advanced inequalities to deal with integrals arising from the derivative of the LKF, thus resulting in a tight upper bound of the derivative of the LKF. By checking the negative definiteness of the upper bound that is a quadratic function in the time-delay, a novel delay-dependent stability result is derived. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones.

[1]  Hanyong Shao,et al.  Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

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

[3]  Qing-Long Han,et al.  State Estimation for Static Neural Networks With Time-Varying Delays Based on an Improved Reciprocally Convex Inequality , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[4]  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).

[5]  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.

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

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

[8]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[9]  Derong Liu,et al.  Qualitative Analysis and Synthesis of Recurrent Neural Networks , 2002 .

[10]  Sang-Moon Lee,et al.  Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality , 2018, J. Frankl. Inst..

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

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

[13]  Derui Ding,et al.  An overview of recent developments in Lyapunov-Krasovskii functionals and stability criteria for recurrent neural networks with time-varying delays , 2018, Neurocomputing.

[14]  PooGyeon Park,et al.  Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays , 2018, J. Frankl. Inst..

[15]  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..

[16]  Qing-Long Han,et al.  Neuronal State Estimation for Neural Networks With Two Additive Time-Varying Delay Components , 2017, IEEE Transactions on Cybernetics.

[17]  Hanyong Shao,et al.  Less conservative delay-dependent stability criteria for neural networks with time-varying delays , 2010, Neurocomputing.

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

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

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

[21]  Qing-Long Han,et al.  Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

[23]  Jin-Hoon Kim,et al.  Further improvement of Jensen inequality and application to stability of time-delayed systems , 2016, Autom..

[24]  Zhigang Zeng,et al.  Hierarchical Type Stability Criteria for Delayed Neural Networks via Canonical Bessel–Legendre Inequalities , 2018, IEEE Transactions on Cybernetics.

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

[26]  Hanyong Shao,et al.  Novel Delay-Dependent Stability Results for Neural Networks with Time-Varying Delays , 2010, Circuits Syst. Signal Process..

[27]  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.

[28]  Jia Wang,et al.  Event-Triggered Generalized Dissipativity Filtering for Neural Networks With Time-Varying Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Jun Wang,et al.  Stability analysis of delayed neural networks via a new integral inequality , 2017, Neural Networks.

[30]  Hanyong Shao,et al.  Improved delay-dependent stability result for neural networks with time-varying delays. , 2018, ISA transactions.

[31]  Dong Yue,et al.  Delay-dependent stability analysis for neural networks with additive time-varying delay components , 2013 .

[32]  Shengyuan Xu,et al.  Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov–Krasovskii Functionals , 2015, IEEE Transactions on Neural Networks and Learning Systems.

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

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

[35]  Hanyong Shao,et al.  Delay-Dependent Approaches to Globally Exponential Stability for Recurrent Neural Networks , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[36]  Jinde Cao,et al.  Global exponential stability and dissipativity of generalized neural networks with time-varying delay signals , 2017, Neural Networks.

[37]  Qing-Long Han,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-Varying Delay Components , 2011, IEEE Transactions on Neural Networks.

[38]  Zhen Wang,et al.  Further results on sampled-data synchronization control for chaotic neural networks with actuator saturation , 2019, Neurocomputing.

[39]  Zhang Yi,et al.  Selectable and Unselectable Sets of Neurons in Recurrent Neural Networks With Saturated Piecewise Linear Transfer Function , 2011, IEEE Transactions on Neural Networks.

[40]  Bo Wang,et al.  New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals , 2017, Appl. Math. Comput..

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

[42]  S. M. Lee,et al.  New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays , 2014 .

[43]  Zhiqiang Zuo,et al.  On exponential stability analysis for neural networks with time-varying delays and general activation functions , 2012 .

[44]  Huaguang Zhang,et al.  Stability criterion for delayed neural networks via Wirtinger-based multiple integral inequality , 2016, Neurocomputing.

[45]  Yibo Wang,et al.  Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov-Krasovskii functional , 2019, Neurocomputing.

[46]  Hanyong Shao,et al.  Improved Delay-Dependent Globally Asymptotic Stability Criteria for Neural Networks With a Constant Delay , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[47]  S. Zhong,et al.  Stability analysis of neutral type neural networks with mixed time-varying delays using triple-integral and delay-partitioning methods. , 2015, ISA transactions.