Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks

This paper studies the robust stability analysis for a class of memristive-based neural networks (NN). The NN consists of a fractional order neutral type quaternion-valued leaky integrator echo state with parameter uncertainties and time-varying delays. First, the quaternion-valued leaky integrator echo state NN with QUAD vector field activation function is transformed into a real-valued system using a linear mapping function. Then, the Lyapunov-Krasovskii functional is adopted to derive the sufficient conditions on the existence and uniqueness of Filippov solution of the NN equilibrium point. The delay-dependent robust stability analysis of such NN is provided with the help of linear matrix inequality technique. Finally, the theoretical results are validated by means of a numerical example.

[1]  Jinde Cao,et al.  Global dissipativity analysis for delayed quaternion-valued neural networks , 2017, Neural Networks.

[2]  Zhigang Zeng,et al.  Global Mittag–Leffler Stabilization of Fractional-Order Memristive Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Lixiang Li,et al.  Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks , 2018, Commun. Nonlinear Sci. Numer. Simul..

[4]  Jinde Cao,et al.  Existence and Uniform Stability Analysis of Fractional-Order Complex-Valued Neural Networks With Time Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Jinde Cao,et al.  LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays , 2018, Int. J. Syst. Sci..

[6]  Jack K. Hale,et al.  Strong stabilization of neutral functional differential equations , 2002 .

[7]  Helmut Hauser,et al.  Echo state networks with filter neurons and a delay&sum readout , 2010, Neural Networks.

[8]  Chuandong Li,et al.  Robust stability of stochastic fuzzy delayed neural networks with impulsive time window , 2015, Neural Networks.

[9]  Zhigang Zeng,et al.  Global Asymptotic Stability and Adaptive Ultimate Mittag–Leffler Synchronization for a Fractional-Order Complex-Valued Memristive Neural Networks With Delays , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[10]  Xiaofeng Chen,et al.  Robust stability analysis of quaternion-valued neural networks via LMI approach , 2018 .

[11]  J. A. Tenreiro Machado,et al.  Chaos suppression in fractional systems using adaptive fractional state feedback control , 2017 .

[12]  Jun Tan,et al.  Boundedness and periodicity for linear threshold discrete-time quaternion-valued neural network with time-delays , 2017, Neurocomputing.

[13]  Yongqing Yang,et al.  Different impulsive effects on synchronization of fractional-order memristive BAM neural networks , 2018 .

[14]  Jinde Cao,et al.  Delay-Independent Stability of Riemann–Liouville Fractional Neutral-Type Delayed Neural Networks , 2017, Neural Processing Letters.

[15]  Jinde Cao,et al.  Robust H∞ control for nonhomogeneous Markovian jump systems subject to quantized feedback and probabilistic measurements , 2018, J. Frankl. Inst..

[16]  S. Abbas,et al.  Global Mittag–Leffler stability of complex valued fractional-order neural network with discrete and distributed delays , 2016, Rendiconti del Circolo Matematico di Palermo Series 2.

[17]  Nobuyuki Matsui,et al.  Quaternion Neural Network and Its Application , 2003, KES.

[18]  Sundarapandian Vaidyanathan,et al.  Computational Intelligence Applications in Modeling and Control , 2015, Computational Intelligence Applications in Modeling and Control.

[19]  Jiabin Wang,et al.  Functional echo state network for time series classification , 2016, Inf. Sci..

[20]  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.

[21]  Xin Wang,et al.  Delay-dependent robust stability and stabilization of uncertain memristive delay neural networks , 2014, Neurocomputing.

[22]  Jang Myung Lee,et al.  Fuzzy Echo State Neural Networks and Funnel Dynamic Surface Control for Prescribed Performance of a Nonlinear Dynamic System , 2014, IEEE Transactions on Industrial Electronics.

[23]  Sanyi Tang,et al.  Robust stability analysis of impulsive complex-valued neural networks with time delays and parameter uncertainties , 2017, Journal of Inequalities and Applications.

[24]  Qiankun Song,et al.  Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties , 2017, Neural Networks.

[25]  Haipeng Peng,et al.  Finite-time projective synchronization of memristor-based delay fractional-order neural networks , 2017 .

[26]  Mario di Bernardo,et al.  On QUAD, Lipschitz, and Contracting Vector Fields for Consensus and Synchronization of Networks , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Shu-Xian Lun,et al.  A new echo state network with variable memory length , 2016, Inf. Sci..

[28]  Naotake Kamiura,et al.  Associative Memory in quaternionic Hopfield Neural Network , 2008, Int. J. Neural Syst..

[29]  Daniel W. C. Ho,et al.  Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach , 2016, IEEE Transactions on Cybernetics.

[30]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[31]  Nobuyuki Matsui,et al.  Quaternionic multistate Hopfield neural network with extended projection rule , 2016, Artificial Life and Robotics.

[32]  I. Carro-Pérez,et al.  Experimental verification of a memristive neural network , 2018 .

[33]  Yaochu Jin,et al.  Modeling neural plasticity in echo state networks for classification and regression , 2016, Inf. Sci..

[34]  Ruya Samli,et al.  A new delay-independent condition for global robust stability of neural networks with time delays , 2015, Neural Networks.

[35]  Jinde Cao,et al.  Quantized H∞ filtering for switched linear parameter-varying systems with sojourn probabilities and unreliable communication channels , 2018, Inf. Sci..

[36]  Yuting Zhang,et al.  Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances , 2018, Physica A: Statistical Mechanics and its Applications.

[37]  Jinde Cao,et al.  Further synchronization in finite time analysis for time-varying delayed fractional order memristive competitive neural networks with leakage delay , 2018, Neurocomputing.

[38]  Nobuyuki Matsui,et al.  Quaternion neural network with geometrical operators , 2004, J. Intell. Fuzzy Syst..

[39]  Hiromi Kusamichi,et al.  A New Scheme for Color Night Vision by Quaternion Neural Network , 2004 .

[40]  Jinde Cao,et al.  Stability and synchronization of fractional-order memristive neural networks with multiple delays , 2017, Neural Networks.

[41]  Jinde Cao,et al.  Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays , 2014, Nonlinear Dynamics.

[42]  Long Cheng,et al.  A Neutral-Type Delayed Projection Neural Network for Solving Nonlinear Variational Inequalities , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[43]  Zhigang Zeng,et al.  Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[44]  Junzhi Yu,et al.  LMI Conditions for Global Stability of Fractional-Order Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[45]  Qiankun Song,et al.  Design and Analysis of Quaternion-Valued Neural Networks for Associative Memories , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[46]  O. Nelles.  Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models , 2000 .

[47]  Mark J. Balas,et al.  Normal Form for Linear Infinite-Dimensional Systems in Hilbert Space and Its Role in Direct Adaptive Control of Distributed Parameter Systems , 2017 .

[48]  Xuyang Lou,et al.  New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks , 2006, Neurocomputing.

[49]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

[50]  Jinde Cao,et al.  Stability Analysis of Quaternion-Valued Neural Networks: Decomposition and Direct Approaches , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[51]  Guoqiang Peter Zhang,et al.  Neural networks for classification: a survey , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[52]  Zhengwen Tu,et al.  Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays , 2017, Neural Processing Letters.

[53]  Sanyi Tang,et al.  Robust stability analysis of impulsive complex-valued neural networks with mixed time delays and parameter uncertainties , 2018 .

[54]  Yongguang Yu,et al.  Dynamical behaviors analysis of memristor-based fractional-order complex-valued neural networks with time delay , 2018, Appl. Math. Comput..

[55]  M. Rivero,et al.  Fractional calculus: A survey of useful formulas , 2013, The European Physical Journal Special Topics.

[56]  Jinde Cao,et al.  Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties , 2019, Appl. Math. Comput..

[57]  Chunyu Yang,et al.  Delay-dependent robust stability for Hopfield neural networks of neutral-type , 2009, Neurocomputing.

[58]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[59]  Qiankun Song,et al.  Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons , 2018 .

[60]  Herbert Jaeger,et al.  Optimization and applications of echo state networks with leaky- integrator neurons , 2007, Neural Networks.

[61]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[62]  Kun She,et al.  Extended robust global exponential stability for uncertain switched memristor-based neural networks with time-varying delays , 2018, Appl. Math. Comput..

[63]  Fuad E. Alsaadi,et al.  Global μ-stability of quaternion-valued neural networks with non-differentiable time-varying delays , 2017, Neurocomputing.

[64]  Zhen Wang,et al.  Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function , 2018, Nonlinear Dynamics.

[65]  Jinde Cao,et al.  Stability analysis of memristor-based fractional-order neural networks with different memductance functions , 2014, Cognitive Neurodynamics.

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

[67]  Oscar Castillo,et al.  Interval type-2 fuzzy weight adjustment for backpropagation neural networks with application in time series prediction , 2014, Inf. Sci..

[68]  Jinyu Li,et al.  Global Mittag-Leffler stabilization of fractional-order complex-valued memristive neural networks , 2018, Appl. Math. Comput..

[69]  Jinde Cao,et al.  Global μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays , 2016, Inf. Sci..

[70]  Jinde Cao,et al.  Stability and Hopf bifurcation analysis of fractional-order complex-valued neural networks with time delays , 2017, Advances in Difference Equations.

[71]  Sibel Senan,et al.  Robustness analysis of uncertain dynamical neural networks with multiple time delays , 2015, Neural Networks.

[72]  Jinde Cao,et al.  Stability analysis of fractional-order delayed neural networks , 2017 .

[73]  Lincong Luo,et al.  Color Image Compression Based on Quaternion Neural Network Principal Component Analysis , 2010, 2010 International Conference on Multimedia Technology.

[74]  Xiaofan Li,et al.  Finite-time synchronization of fractional-order memristive recurrent neural networks with discontinuous activation functions , 2018, Neurocomputing.

[75]  Jun Wang,et al.  Chaotic Time Series Prediction Based on a Novel Robust Echo State Network , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[76]  Haijun Jiang,et al.  Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks , 2018, Neural Networks.

[77]  J. A. Tenreiro Machado,et al.  Dynamic stability analysis of fractional order leaky integrator echo state neural networks , 2017, Commun. Nonlinear Sci. Numer. Simul..

[78]  Jinde Cao,et al.  Stability analysis of fractional-order complex-valued neural networks with time delays☆ , 2015 .

[79]  José António Tenreiro Machado,et al.  Uniform stability of Fractional Order Leaky Integrator Echo State Neural Network with multiple time delays , 2017, Inf. Sci..

[80]  J. A. Tenreiro Machado,et al.  Fractional generalization of memristor and higher order elements , 2013, Commun. Nonlinear Sci. Numer. Simul..

[81]  Herbert Jaeger,et al.  Reservoir computing approaches to recurrent neural network training , 2009, Comput. Sci. Rev..

[82]  Zhigang Zeng,et al.  Global Uniform Asymptotic Fixed Deviation Stability and Stability for Delayed Fractional-order Memristive Neural Networks with Generic Memductance , 2018, Neural Networks.

[83]  Zhenjiang Zhao,et al.  Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with both leakage and time-varying delays , 2017, Neurocomputing.

[84]  Jinde Cao,et al.  Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay , 2017, Neural Networks.