Abstract
This paper investigates the state estimation problem for a class of fractional-order memristive neural networks (FOMNNs) with leakage and time delay. The main objective of this study is to construct an efficient estimator such that the state of the corresponding estimation error is globally stable. Distinct to the previous studies, the state estimation problem of FOMNNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global stability of the error system has been derived as a set of solvable linear matrix inequalities. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated.
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Chua L (1971) Memristor-the missing circuit element. IEEE Trans Circuit Theory 18(5):507–519
Yang S, Guo Z, Wang J (2015) Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling. IEEE Trans Syst Man Cybern Syst 45(7):1077–1086
Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453(7191):80–83
Kim H, Sah MP, Yang C, Roska T, Chua LO (2011) Neural synaptic weighting with a pulse-based memristor circuit. IEEE Trans Circuits Syst I Regul Pap 59(1):148–158
Kim H, Sah MP, Yang C, Chua LO (2010) Memristor-based multilevel memory. In: 2010 12th international workshop on cellular nanoscale networks and their applications (CNNA 2010). IEEE, pp 1–6
Kim H, Sah MP, Yang C, Roska T, Chua LO (2011) Memristor bridge synapses. Proc IEEE 100(6):2061–2070
Wang B, Zou FC, Cheng J (2018) A memristor-based chaotic system and its application in image encryption. Optik 154:538–544
Li KZ, Zhao MC, Fu XC (2009) Projective synchronization of driving-response systems and its application to secure communication. IEEE Trans Circuits Syst I Regul Pap 56(10):2280–2291
Lunstrom BN, Higgs MH, Spain WJ, Fairhall AL (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11(11):1335
Anastassiou GA (2012) Fractional neural network approximation. Comput Math Appl 64(6):1655–1676
Zhou S, Li H, Zhu Z (2008) Chaos control and synchronization in a fractional neuron network system. Chaos Solitons Fractals 36(4):973–984
Wang H, Yu Y, Wen G, Zhang S, Yu J (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23
Deng W, Li C, Lü J (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409–416
Zhang S, Yu Y, Yu J (2016) LMI conditions for global stability of fractional-order neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2423–2433
Zhang H, Ye R, Liu S, Cao J, Alsaedi A, Li X (2018) LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays. Int J Syst Sci 49(3):537–545
Yang Y, He Y, Wang Y, Wu M (2018) Stability analysis of fractional-order neural networks: an LMI approach. Neurocomputing 285:82–93
Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhao H (2016) Finite-time stability and synchronization for memristor-based fractional-order Cohen–Grossberg neural network. Eur Phys J B 89(9):204
Bao H, Cao J (2017) State estimation of fractional-order neural networks with time delay. In: 2017 Chinese automation congress (CAC). IEEE, pp 1573–1577
Yang D, Hu C, Wang Z, Liang X (2008) New global stability criteria of neural networks with time delays. In: 2008 7th world congress on intelligent control and automation. IEEE, pp 5317–5320
Arik S (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays. IEEE Trans Neural Netw 16(3):580–586
Cao J (2003) Global asymptotic stability of delayed bi-directional associative memory neural networks. Appl Math Comput 142(2–3):333–339
Zhang Z, Zhang J, Ai Z (2019) A novel stability criterion of the time-lag fractional-order gene regulatory network system for stability analysis. Commun Nonlinear Sci Numer Simul 66:96–108
Lakshmanan S, Park JH, Jung HY, Balasubramaniam P (2012) Design of state estimator for neural networks with leakage, discrete and distributed delays. Appl Math Comput 218(22):11297–11310
Podlubny I (1999) Fractional differential equations. Academic Press, San Diego
Zhang S, Yu Y, Wang H (2015) Mittag-Leffler stability of fractional-order Hopfield neural networks. Nonlinear Anal Hybrid Syst 16:104–121
Liu H, Wang Z (2017) Event-triggered \(H_{\infty }\) state estimation for delayed stochastic memristive neural networks with missing measurements: The discrete time case. IEEE Trans Neural Netw Learn Syst 28(12):3815–3825
Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667–675
Xu J, Cao YY, Sun Y, Tang J (2008) Absolute exponential stability of recurrent neural networks with generalized activation function. IEEE Trans Neural Netw 19(6):1075–1089
Song C, Cao J (2014) Dynamics in fractional-order neural networks. Neurocomputing 142:494–498
Jarad F, Abdeljawad T, Baleanu D (2013) Stability of q-fractional non-autonomous systems. Nonlinear Anal Real World Appl 14(1):780–784
Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9):2860–2866
Liang S, Wu R, Chen L (2016) Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay. Phys A Stat Mech Appl 444:49–62
Wu H, Zhang X, Xue S, Wang L, Wang Y (2016) LMI conditions to global Mittag–Leffler stability of fractional-order neural networks with impulses. Neurocomputing 193:148–154
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Nagamani, G., Shafiya, M. & Soundararajan, G. An LMI Based State Estimation for Fractional-Order Memristive Neural Networks with Leakage and Time Delays. Neural Process Lett 52, 2089–2108 (2020). https://doi.org/10.1007/s11063-020-10338-0
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DOI: https://doi.org/10.1007/s11063-020-10338-0