Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties

Abstract This paper focuses on the robust stability analysis of fractional-order quaternion-valued neural networks (FOQVNNs) with neutral delay and parameter uncertainties. Without transforming the FOQVNNs into equivalent two complex-valued systems or four real-valued systems, based on homeomorphism principle, matrix inequality technique and Lyapunov method, both delay-independent and delay-dependent criteria to guarantee the existence, uniqueness and global stability of equilibrium point for the considered FOQVNNs are derived in the form of linear matrix inequality (LMI). Two examples with simulations are provided to manifest the theoretical results.

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

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

[3]  Jitao Sun,et al.  Stability of Quaternion-Valued Neural Networks with Mixed Delays , 2018, Neural Processing Letters.

[4]  Yonggang Chen,et al.  Exponential Synchronization for Delayed Dynamical Networks via Intermittent Control: Dealing With Actuator Saturations , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Taotao Hu,et al.  Finite-time stability for fractional-order complex-valued neural networks with time delay , 2020, Appl. Math. Comput..

[6]  Hari M. Srivastava,et al.  Global exponential stability of fractional‐order impulsive neural network with time‐varying and distributed delay , 2018 .

[7]  Manchun Tan,et al.  Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions , 2019, Appl. Math. Comput..

[8]  Wei Chen,et al.  Distributed Resilient Filtering for Power Systems Subject to Denial-of-Service Attacks , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[9]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[10]  Swati Tyagi,et al.  Finite-time stability for a class of fractional-order fuzzy neural networks with proportional delay , 2020, Fuzzy Sets Syst..

[11]  Ruya Samli,et al.  Some generalized global stability criteria for delayed Cohen-Grossberg neural networks of neutral-type , 2019, Neural Networks.

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

[13]  Jinde Cao,et al.  Stability and pinning synchronization analysis of fractional order delayed Cohen-Grossberg neural networks with discontinuous activations , 2019, Appl. Math. Comput..

[14]  Muthukumar Palanisamy,et al.  Existence, uniqueness, and global asymptotic stability analysis for delayed complex-valued Cohen–Grossberg BAM neural networks , 2018, Neural Computing and Applications.

[15]  E. Suntonsinsoungvon,et al.  Exponential stability of discrete-time uncertain neural networks with multiple time-varying leakage delays , 2020, Math. Comput. Simul..

[16]  Qing-Long Han,et al.  Neural-network-based output-feedback control with stochastic communication protocols , 2019, Autom..

[17]  Weisheng Chen,et al.  Exponential stability analysis of quaternion-valued neural networks with proportional delays and linear threshold neurons: Continuous-time and discrete-time cases , 2020, Neurocomputing.

[18]  Neyir Ozcan,et al.  Stability analysis of Cohen-Grossberg neural networks of neutral-type: Multiple delays case , 2019, Neural Networks.

[19]  Zhenjiang Zhao,et al.  Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Jinde Cao,et al.  Finite-time Stability of Fractional-order Complex-valued Neural Networks with Time Delays , 2017, Neural Processing Letters.

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

[22]  Qing-Long Han,et al.  A Recursive Approach to Quantized ${H_{\infty}}$ State Estimation for Genetic Regulatory Networks Under Stochastic Communication Protocols , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Sabri Arik,et al.  A modified Lyapunov functional with application to stability of neutral-type neural networks with time delays , 2019, J. Frankl. Inst..

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

[25]  Jinde Cao,et al.  Quasi-state estimation and quasi-synchronization control of quaternion-valued fractional-order fuzzy memristive neural networks: Vector ordering approach , 2019, Appl. Math. Comput..

[26]  Haijun Jiang,et al.  Finite-time synchronization of fully complex-valued neural networks with fractional-order , 2020, Neurocomputing.

[27]  R. Wu,et al.  Finite-Time Stability of Fractional-Order Neural Networks with Delay , 2013 .

[28]  Wei Zhang,et al.  Stability analysis of quaternion-valued neural networks with both discrete and distributed delays , 2019, Appl. Math. Comput..

[29]  Shiping Wen,et al.  New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality , 2019, Neural Networks.

[30]  Jinde Cao,et al.  Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach , 2018 .

[31]  I. Podlubny.  Fractional differential equations , 1998 .

[32]  PooGyeon Park,et al.  A combined reciprocal convexity approach for stability analysis of static neural networks with interval time-varying delays , 2017, Neurocomputing.

[33]  Jinde Cao,et al.  Global synchronization of fractional-order quaternion-valued neural networks with leakage and discrete delays , 2020, Neurocomputing.

[34]  Fuad E. Alsaadi,et al.  Partial-Nodes-Based State Estimation for Complex Networks With Unbounded Distributed Delays , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Fuad E. Alsaadi,et al.  Global exponential stability in Lagrange sense for quaternion-valued neural networks with leakage delay and mixed time-varying delays , 2019, Int. J. Syst. Sci..

[36]  Fuad E. Alsaadi,et al.  Fusion estimation for multi-rate linear repetitive processes under weighted try-once-discard protocol , 2020, Inf. Fusion.

[37]  Jinde Cao,et al.  Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays , 2019, Neural Networks.

[38]  Qing-Long Han,et al.  A Set-Membership Approach to Event-Triggered Filtering for General Nonlinear Systems Over Sensor Networks , 2020, IEEE Transactions on Automatic Control.

[39]  Qiankun Song,et al.  Multistability Analysis of Quaternion-Valued Neural Networks With Time Delays , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Song Zhu,et al.  Leakage delay-dependent stability analysis for complex-valued neural networks with discrete and distributed time-varying delays , 2019, Neurocomputing.

[41]  Fuad E. Alsaadi,et al.  Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties , 2018, Neural Networks.

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

[43]  Jinde Cao,et al.  Exponential input-to-state stability of quaternion-valued neural networks with time delay , 2019, Appl. Math. Comput..