Global lagrange stability of complex-valued neural networks of neutral type with time-varying delays

In this article, the problem of global exponential stability in Lagrange sense of neutral type complex-valued neural networks (CVNNs) with delays is investigated. Two different classes of activation functions are considered, one can be separated into real part and imaginary part, and the other cannot be separated. Based on Lyapunov theory and analytic techniques, delay-dependent criteria are provided to ascertain the aforementioned CVNNs to be globally exponentially stable GES in Lagrange sense. Moreover, the proposed sufficient conditions are presented in the form of linear matrix inequalities which could be easily checked by Matlab. Finally, two simulation examples are given out to demonstrate the validity of theory results. © 2016 Wiley Periodicals, Inc. Complexity 21: 438–450, 2016

[1]  Peng Shi,et al.  Adaptive Synchronization for Neutral-Type Neural Networks with Stochastic Perturbation and Markovian Switching Parameters , 2014, IEEE Transactions on Cybernetics.

[2]  Jinde Cao,et al.  Exponential H∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities , 2016, Science China Technological Sciences.

[3]  Jun Wang,et al.  Global Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[4]  P. Balasubramaniam,et al.  Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations , 2011 .

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

[6]  Jinde Cao,et al.  Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Tao Fan,et al.  Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties , 2014, Complex..

[8]  Zhenjiang Zhao,et al.  Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays , 2015, Neurocomputing.

[9]  Jinde Cao,et al.  Global μ-stability of complex-valued delayed neural networks with leakage delay , 2015, Neurocomputing.

[10]  R. Rakkiyappan,et al.  Stability analysis of memristor-based complex-valued recurrent neural networks with time delays , 2016, Complex..

[11]  Guodong Zhang,et al.  Global exponential stability in a Lagrange sense for memristive recurrent neural networks with time-varying delays , 2015, Neurocomputing.

[12]  Zhigang Zeng,et al.  Lagrange Stability of Memristive Neural Networks With Discrete and Distributed Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Ju H. Park,et al.  Non-fragile H∞ synchronization of memristor-based neural networks using passivity theory , 2016, Neural Networks.

[14]  Ju H. Park,et al.  A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays , 2013, Neurocomputing.

[15]  Zhigang Zeng,et al.  Multistability of Neural Networks With Time-Varying Delays and Concave-Convex Characteristics , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[17]  Jinde Cao,et al.  Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays , 2016, Neurocomputing.

[18]  Zhigang Zeng,et al.  Positive invariant and global exponential attractive sets of neural networks with time-varying delays , 2008, Neurocomputing.

[19]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[20]  Bo Zhou,et al.  Boundedness and complete stability of complex-valued neural networks with time delay. , 2013, IEEE transactions on neural networks and learning systems.

[21]  Tingwen Huang,et al.  Exponential estimates and exponential stability for neutral-type neural networks with multiple delays , 2015, Neurocomputing.

[22]  Ju H. Park,et al.  Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control , 2015, Complex..

[23]  R. Brayton.  Bifurcation of periodic solutions in a nonlinear difference-differential equations of neutral type , 1966 .

[24]  Sabri Arik,et al.  An analysis of stability of neutral-type neural systems with constant time delays , 2014, J. Frankl. Inst..

[25]  Donq-Liang Lee,et al.  Relaxation of the stability condition of the complex-valued neural networks , 2001, IEEE Trans. Neural Networks.

[26]  Z. Zeng,et al.  Global exponential stability in Lagrange sense for recurrent neural networks with time delays , 2008 .

[27]  Wei Jiang,et al.  Almost periodic solutions for neutral type BAM neural networks with distributed leakage delays on time scales , 2015, Neurocomputing.

[28]  Zhigang Zeng,et al.  Lagrange stability of neural networks with memristive synapses and multiple delays , 2014, Inf. Sci..

[29]  Akira Hirose,et al.  Generalization Characteristics of Complex-Valued Feedforward Neural Networks in Relation to Signal Coherence , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Jacek M. Zurada,et al.  Complex-valued multistate neural associative memory , 1996, IEEE Trans. Neural Networks.

[31]  Jigui Jian,et al.  Global Lagrange stability for neutral-type Cohen-Grossberg BAM neural networks with mixed time-varying delays , 2015, Math. Comput. Simul..

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

[33]  Nobuyuki Matsui,et al.  Quaternionic Neural Networks: Fundamental Properties and Applications , 2009 .

[34]  Hao Shen,et al.  Multiple-interval-dependent robust stability analysis for uncertain stochastic neural networks with mixed-delays , 2015, Complex..

[35]  Jinde Cao,et al.  Bifurcations in a delayed fractional complex-valued neural network , 2017, Appl. Math. Comput..

[36]  Jinde Cao,et al.  Analysis of global O(t-α) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays , 2016, Neural Networks.

[37]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[38]  Xiaodi Li,et al.  Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays , 2015, Inf. Sci..

[39]  Qiankun Song,et al.  Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales , 2013, Neurocomputing.

[40]  Pagavathigounder Balasubramaniam,et al.  An LMI approach for global robust dissipativity analysis of T-S fuzzy neural networks with interval time-varying delays , 2012, Expert Syst. Appl..