Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov-Krasovskii functional

Abstract This paper examines the problem of asymptotic stability of continuous neural networks with time-varying delay via a new Lyapunov–Krasovskii functional (LKF). First, a suitable quadratic functional is constructed, which coordinates with the use of the orthogonal-polynomials-based integral inequality. Second, the novel proposed LKF contains more state vectors of neural networks, so that more state information can be exploited adequately. By combining the new proposed LKF and orthogonal-polynomials-based integral inequality, novel delay-dependent stability criteria with less conservatism are established in the form of linear matrix inequalities (LMIs). Finally, two commonly-used numerical examples are provided to show the effectiveness and improvement of the proposed criteria.

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

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

[3]  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.

[4]  Ju H. Park,et al.  Further results on stabilization of neural-network-based systems using sampled-data control , 2017 .

[5]  Fuad E. Alsaadi,et al.  Finite-Time State Estimation for Recurrent Delayed Neural Networks With Component-Based Event-Triggering Protocol , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Xiaodong Liu,et al.  Improved delay-dependent stability criteria for generalized neural networks with time-varying delays , 2017, Inf. Sci..

[7]  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.

[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]  Qing-Long Han,et al.  Global Asymptotic Stability for Delayed Neural Networks Using an Integral Inequality Based on Nonorthogonal Polynomials , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Xin-Ping Guan,et al.  New robust stability condition for discrete-time recurrent neural networks with time-varying delays and nonlinear perturbations , 2017, Neurocomputing.

[11]  Tingwen Huang,et al.  An Event-Triggered Approach to State Estimation for a Class of Complex Networks With Mixed Time Delays and Nonlinearities , 2016, IEEE Transactions on Cybernetics.

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

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

[14]  Ju H. Park,et al.  Stability Analysis of Neural Networks With Time-Varying Delay by Constructing Novel Lyapunov Functionals , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

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

[17]  Huaicheng Yan,et al.  Improved Stability Analysis for Delayed Neural Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Xian Wei,et al.  Exponential synchronization of a class of neural networks with sampled-data control , 2017, Appl. Math. Comput..

[19]  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..

[20]  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.

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

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

[23]  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..

[24]  Yong He,et al.  Delay-Variation-Dependent Stability of Delayed Discrete-Time Systems , 2016, IEEE Transactions on Automatic Control.

[25]  Yong He,et al.  Notes on Stability of Time-Delay Systems: Bounding Inequalities and Augmented Lyapunov-Krasovskii Functionals , 2017, IEEE Transactions on Automatic Control.

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

[27]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

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

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

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

[31]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[32]  Yin Sheng,et al.  Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

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

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

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