Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay

The objective of this paper is to analyze the stability analysis of neutral-type neural networks with additive time-varying delay and leakage delay. By constructing a suitable augmented Lyapunov-Krasovskii functional with triple and four integral terms, some new stability criteria are established in terms of linear matrix inequalities, which is easily solved by various convex optimization techniques. More information of the lower and upper delay bounds of time-varying delays are used to derive the stability criteria, which can lead less conservative results. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasible can be checked easily by MATLAB LMI control toolbox. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

[1]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

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

[3]  S. Hara,et al.  Repetitive control system: a new type servo system for periodic exogenous signals , 1988 .

[4]  K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[5]  Bart Kosko,et al.  Neural networks and fuzzy systems , 1998 .

[6]  S. Niculescu Delay Effects on Stability: A Robust Control Approach , 2001 .

[7]  X. Zou,et al.  Harmless delays in Cohen–Grossberg neural networks ☆ , 2002 .

[8]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[9]  K. Gopalsamy Leakage delays in BAM , 2007 .

[10]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[11]  Yu Zhao,et al.  Asymptotic stability analysis of neural networks with successive time delay components , 2008, Neurocomputing.

[12]  Dong Yue,et al.  New stability criteria of neural networks with interval time-varying delay: A piecewise delay method , 2009, Appl. Math. Comput..

[13]  Ju H. Park,et al.  Improved delay-dependent stability criterion for neural networks with time-varying delays , 2009 .

[14]  Shengyuan Xu,et al.  Delay-dependent stability of neutral type neural networks with distributed delays , 2009, Neurocomputing.

[15]  Hieu Minh Trinh,et al.  Exponential Stabilization of Neural Networks With Various Activation Functions and Mixed Time-Varying Delays , 2010, IEEE Transactions on Neural Networks.

[16]  Zhigang Zeng,et al.  Global exponential stability in Lagrange sense for neutral type recurrent neural networks , 2011, Neurocomputing.

[17]  Shouming Zhong,et al.  Improved delay-dependent stability criterion for neural networks with time-varying delay , 2011, Appl. Math. Comput..

[18]  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.

[19]  Xiaodi Li,et al.  Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations , 2011, J. Frankl. Inst..

[20]  Aiguo Song,et al.  Stability analysis on delayed neural networks based on an improved delay-partitioning approach , 2011, J. Comput. Appl. Math..

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

[22]  Guoshan Zhang,et al.  Non-fragile robust finite-time H∞ control for nonlinear stochastic itô systems using neural network , 2012 .

[23]  Zeynep Orman,et al.  New sufficient conditions for global stability of neutral-type neural networks with time delays , 2012, Neurocomputing.

[24]  Y. Kuang Delay Differential Equations: With Applications in Population Dynamics , 2012 .

[25]  Shumin Fei,et al.  RBF neural networks-based robust adaptive tracking control for switched uncertain nonlinear systems , 2012 .

[26]  Shouming Zhong,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components , 2012 .

[27]  K. Mathiyalagan,et al.  An improved delay-dependent criterion for stability of uncertain neutral systems with mixed time delays , 2013 .

[28]  Pin-Lin Liu,et al.  Improved delay-dependent stability of neutral type neural networks with distributed delays. , 2013, ISA transactions.

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

[30]  Xiaodi Li,et al.  Effect of leakage time-varying delay on stability of nonlinear differential systems , 2013, J. Frankl. Inst..

[31]  Yingmin Jia,et al.  New approaches on stability criteria for neural networks with two additive time-varying delay components , 2013, Neurocomputing.

[32]  Yang Tang,et al.  Synchronization of Nonlinear Dynamical Networks With Heterogeneous Impulses , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  Xiaodi Li,et al.  Global exponential stability of a class of impulsive cellular neural networks with supremums , 2014 .

[34]  Ju H. Park,et al.  Delay fractioning approach to robust exponential stability of fuzzy Cohen-Grossberg neural networks , 2014, Appl. Math. Comput..

[35]  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..

[36]  Sabri Arik,et al.  An improved robust stability result for uncertain neural networks with multiple time delays , 2014, Neural Networks.

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

[38]  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.

[39]  R. Rakkiyappan,et al.  Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays , 2015 .

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

[41]  Ju H. Park,et al.  Stability of time-delay systems via Wirtinger-based double integral inequality , 2015, Autom..

[42]  Jinde Cao,et al.  New delay-dependent stability criteria for switched Hopfield neural networks of neutral type with additive time-varying delay components , 2015, Neurocomputing.

[43]  Xinzhi Liu,et al.  New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays , 2015, Neurocomputing.

[44]  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.

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

[46]  Muthukumar Palanisamy,et al.  Stability criteria for Markovian jump neural networks with mode-dependent additive time-varying delays via quadratic convex combination , 2016, Neurocomputing.

[47]  Feng Jiang,et al.  Exponential stability of stochastic neural networks with leakage delays and expectations in the coefficients , 2016, Neurocomputing.

[48]  Rajendran Samidurai,et al.  Robust passivity analysis for neutral-type neural networks with mixed and leakage delays , 2016, Neurocomputing.

[49]  Jinde Cao,et al.  An Impulsive Delay Inequality Involving Unbounded Time-Varying Delay and Applications , 2017, IEEE Transactions on Automatic Control.