Improved delay-dependent stability criteria for generalized neural networks with time-varying delays

Abstract This paper is concerned with the problem of stability analysis for generalized neural networks with time-varying delays. A novel integral inequality which includes several existing inequalities as special cases is presented. By employing a suitable Lyapunov–Krasovskii functional (LKF) and using the proposed integral inequality to estimate the derivative of the LKF, improved delay-dependent stability criteria expressed in terms of linear matrix inequalities are derived. Finally, four numerical examples are provided to demonstrate the effectiveness and the improvement of the proposed method.

[1]  Jie Chen,et al.  New stability criteria for recurrent neural networks with interval time-varying delay , 2013, Neurocomputing.

[2]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[3]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Leonard Ziemiański,et al.  Neural networks in mechanics of structures and materials – new results and prospects of applications , 2001 .

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

[6]  Xinghuo Yu,et al.  A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Georgi M. Dimirovski,et al.  Delay-dependent stability for neural networks with time-varying delays via a novel partitioning method , 2016, Neurocomputing.

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

[9]  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.

[10]  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.

[11]  Dong Sun Lee,et al.  Strategy and Software Application of Fresh Produce Package Design to Attain Optimal Modified Atmosphere , 2014 .

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

[13]  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.

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

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

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

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

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

[19]  Éva Gyurkovics.  A note on Wirtinger-type integral inequalities for time-delay systems , 2015, Autom..

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

[21]  Shouming Zhong,et al.  Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays , 2014, Neurocomputing.

[22]  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..

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

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

[25]  Xiangjun Xie,et al.  New asymptotic stability criteria for neural networks with time-varying delay , 2010 .

[26]  Yong He,et al.  Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Neural Networks.

[27]  S. M. Lee,et al.  On Less Conservative Stability Criteria for Neural Networks with Time-Varying Delays Utilizing Wirtinger-Based Integral Inequality , 2014 .

[28]  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.

[29]  Ting Wang,et al.  Delay-Derivative-Dependent Stability for Delayed Neural Networks With Unbound Distributed Delay , 2010, IEEE Transactions on Neural Networks.

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

[31]  Tao Li,et al.  Further Results on Delay-Dependent Stability Criteria of Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

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

[33]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[34]  Jin-Hua She,et al.  New results on stability analysis for systems with discrete distributed delay , 2015, Autom..

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

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

[37]  Shen-Ping Xiao,et al.  New Globally Asymptotic Stability Criteria for Delayed Cellular Neural Networks , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  Yuanqing Xia,et al.  Stability analysis of systems with time-varying delays via the second-order Bessel-Legendre inequality , 2017, Autom..

[39]  Fang Xu,et al.  Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays , 2014, Appl. Math. Comput..

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

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

[42]  Yijing Wang,et al.  A New Method for Stability Analysis of Recurrent Neural Networks With Interval Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

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

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

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