Stability analysis of discrete-time neural networks with an interval-like time-varying delay

Abstract This paper studies the stability of discrete-time neural networks with an interval-like time-varying delay via the Lyapunov–Krasovskii (L–K) functional method. Firstly, a general free-matrix-based (GFMB) summation inequality is proposed, which includes the auxiliary-function-based and conventional free-matrix-based ones. Secondly, a novel L–K functional is deliberately constructed to make full advantage of the newly-developed GFMB summation inequality. Finally, a new stability condition is derived and two widely-used numerical examples are presented to show the effectiveness of the proposed approach.

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

[2]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[3]  Huijun Gao,et al.  New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays , 2010, Neurocomputing.

[4]  Kok Lay Teo,et al.  Improved Stability Criteria for Discrete-time Delay Systems via Novel Summation Inequalities , 2018, International Journal of Control, Automation and Systems.

[5]  Ju H. Park,et al.  Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays , 2013, Appl. Math. Comput..

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

[7]  Qing-Long Han,et al.  Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems , 2015, Autom..

[8]  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.

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

[10]  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.

[11]  Qing-Long Han,et al.  An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay , 2017, Autom..

[12]  Pagavathigounder Balasubramaniam,et al.  Robust stability analysis for discrete-time uncertain neural networks with leakage time-varying delay , 2015, Neurocomputing.

[13]  Hong-Hai Lian,et al.  Analysis on robust passivity of uncertain neural networks with time-varying delays via free-matrix-based integral inequality , 2017 .

[14]  Hongye Su,et al.  Improved Delay-Dependent Stability Condition of Discrete Recurrent Neural Networks With Time-Varying Delays , 2010, IEEE Transactions on Neural Networks.

[15]  K. Mathiyalagan,et al.  Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks , 2012 .

[16]  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.

[17]  Hieu Minh Trinh,et al.  Discrete Wirtinger-based inequality and its application , 2015, J. Frankl. Inst..

[18]  Xin-Ge Liu,et al.  Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay , 2016, Neurocomputing.

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

[20]  Shengyuan Xu,et al.  Relaxed passivity conditions for neural networks with time-varying delays , 2014, Neurocomputing.

[21]  Jinde Cao,et al.  Global exponential stability of discrete-time Cohen-Grossberg neural networks , 2005, Neurocomputing.

[22]  Jinde Cao,et al.  Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay , 2017 .

[23]  Junkang Tian,et al.  New stability analysis for generalized neural networks with interval time-varying delays , 2017, International Journal of Control, Automation and Systems.

[24]  Shengyuan Xu,et al.  Two novel general summation inequalities to discrete-time systems with time-varying delay , 2017, J. Frankl. Inst..

[25]  Ju H. Park,et al.  New criteria on delay-dependent stability for discrete-time neural networks with time-varying delays , 2013, Neurocomputing.

[26]  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.

[27]  Emilia Fridman,et al.  Stability of Discrete-Time Systems With Time-Varying Delays via a Novel Summation Inequality , 2015, IEEE Transactions on Automatic Control.

[28]  Shengyuan Xu,et al.  Stability analysis of continuous-time systems with time-varying delay using new Lyapunov-Krasovskii functionals , 2018, J. Frankl. Inst..

[29]  Fang Liu,et al.  Improved Free-Weighting Matrix Approach for Stability Analysis of Discrete-Time Recurrent Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Ju H. Park,et al.  Non-fragile synchronization of neural networks with time-varying delay and randomly occurring controller gain fluctuation , 2013, Appl. Math. Comput..

[31]  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.

[32]  Huijun Gao,et al.  Network-Induced Constraints in Networked Control Systems—A Survey , 2013, IEEE Transactions on Industrial Informatics.

[33]  James Lam,et al.  Stability and Synchronization of Discrete-Time Neural Networks With Switching Parameters and Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Wei Xing Zheng,et al.  A new approach to stability analysis of discrete-time recurrent neural networks with time-varying delay , 2009, Neurocomputing.

[35]  Qing-Guo Wang,et al.  Stability Analysis of Discrete-Time Neural Networks With Time-Varying Delay via an Extended Reciprocally Convex Matrix Inequality , 2017, IEEE Transactions on Cybernetics.

[36]  Ting Wang,et al.  Triple Lyapunov functional technique on delay-dependent stability for discrete-time dynamical networks , 2013, Neurocomputing.

[37]  Jianbin Qiu,et al.  A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[38]  Ju H. Park,et al.  On stability criteria for neural networks with time-varying delay using Wirtinger-based multiple integral inequality , 2015, J. Frankl. Inst..

[39]  Hongye Su,et al.  New results on robust exponential stability for discrete recurrent neural networks with time-varying delays , 2009, Neurocomputing.

[40]  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.

[41]  Yun Zou,et al.  Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays , 2008, Neurocomputing.

[42]  Shengyuan Xu,et al.  Summation inequality and its application to stability analysis for time-delay systems , 2016 .

[43]  Shengyuan Xu,et al.  Novel Summation Inequalities and Their Applications to Stability Analysis for Systems With Time-Varying Delay , 2017, IEEE Transactions on Automatic Control.

[44]  Pagavathigounder Balasubramaniam,et al.  Robust stability analysis for discrete-time neural networks with time-varying leakage delays and random parameter uncertainties , 2016, Neurocomputing.

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

[46]  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.

[47]  Wei Xing Zheng,et al.  Synchronization and State Estimation of a Class of Hierarchical Hybrid Neural Networks With Time-Varying Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[48]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[49]  PooGyeon Park,et al.  Robust Η/ spl alpha/ stabilisation of networked control systems with packet analyser [Brief Paper] , 2010 .

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