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Finite-time stability of CNNs with neutral proportional delays and time-varying leakage delays. (English) Zbl 1356.34074

Summary: In this paper, a class of cellular neural networks with neutral proportional delays and time-varying leakage delays is considered. Some results on the finite-time stability for the equations are obtained by using the differential inequality technique. In addition, an example with numerical simulations is given to illustrate our results, and the generalized exponential synchronization is also established.

MSC:

34K25 Asymptotic theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
34K38 Functional-differential inequalities
Full Text: DOI

References:

[1] PengL, WangW. Anti‐periodic solutions for shunting inhibitory cellular neural networks with time‐varying delays in leakage terms. Neurocomputing2013; 111: 27-33.
[2] XiongW. New result on convergence for HCNNs with time‐varying leakage Delays. Neural Computing and Applications2015; 26: 485-491.
[3] XiongW. New exponential convergence on SICNNs with time‐varying leakage delays and neutral type distributed delays. Journal of Applied Mathematics and Computing2015; 49: 157-179. · Zbl 1328.34072
[4] ZhouQ. Pseudo almost periodic solutions for SICNNs with leakage delays and complex deviating arguments. Neural Processing Letters2015. 10.1007/s11063‐015‐9462‐1.
[5] ZhouL. Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing2015; 161: 99-106.
[6] HuangZ. Almost periodic solutions for fuzzy cellular neural networks with time‐varying delays. Neural Computing and Applications2016. 10.1007/s00521‐016‐2194‐y.
[7] HuangZ. Almost periodic solutions for fuzzy cellular neural networks with time‐varying delays. International Journal of Machine Learning and Cybernetics2016. 10.1007/s13042‐016‐0507‐1.
[8] AmatoF, AmbrosinoR, AriolaM, CosentinoC, De TomasiG. Finite‐Time Stability and Control. Springer‐Verlag: London, 2014. · Zbl 1297.93001
[9] GarciaG, TarbouriechS, BernussouJ. Finite‐time stabilization of linear time‐varying continuous systems. IEEE Transactions on Automatic Control2009; 54: 364-369. · Zbl 1367.93060
[10] AmatoF, AriolaM, CosentinoC. Finite‐time control of discrete‐time linear systems: analysis and design conditions. Automatica2010; 46: 919-924. · Zbl 1191.93099
[11] HeS, LiuF. Observer‐based finite‐time control of time‐delayed jump systems. Applied Mathematics and Computation2010; 217: 2327-2338. · Zbl 1207.93113
[12] XiangW, XiaoJ, IqbalMN. Robust finite‐time bounded observer design for a class of uncertain non‐linear Markovian jump systems. IMA Journal of Mathematical Control and Information2012; 29: 551-572. · Zbl 1256.93025
[13] Le Van HienDoanThaiSon. Finite‐time stability of a class of non‐autonomous neural networks with heterogeneous proportional delays. Applied Mathematics and Computation2015; 251: 14-23. · Zbl 1328.92010
[14] LiuB. Finite‐time stability of a class of CNNs with heterogeneous proportional delays and oscillating leakage coefficients. Neural Processing Letters2016. 10.1007/s11063‐016‐9512‐3.
[15] ChenZ. A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Computing and Applications2013; 23: 2429-2434.
[16] LiuB. Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing2015; 148: 445-454.
[17] LiuX. Exponential convergence of SICNNs with delays and oscillating coefficients in leakage terms. Neurocomputing2015; 168: 500-504.
[18] ZhaoC, WangZ. Exponential convergence of a SICNN with leakage delays and continuously distributed delays of neutral type. Neural Processing Letters2015; 41: 239-247.
[19] YuY. Global exponential convergence for a class of neutral functional differential equations with proportional delays. Mathematical Methods in the Applied Sciences2016. 10.1002/mma.3880. · Zbl 1352.34106
[20] ZhengC, LiN, CaoJ. Matrix measure based stability criteria for high‐order networks with proportional delay. Neurcomputing2015; 149: 1149-1154.
[21] ZhouL. Dissipativity of a class of cellular neural networks with proportional delays. Nonlinear Dynamics2013; 73(3): 1895-1903. · Zbl 1281.92010
[22] ZhouL. Delay‐dependent exponential synchronization of recurrent neural networks with multiple proportional delays. Neural Processing Letters2015; 42(3): 619-632.
[23] WangL, ChenT. Multiple μ‐stability of neural networks with unbounded time‐varying delays. Neural Processing Letters2014; 53: 109-118. · Zbl 1307.93365
[24] SongX, ZhaoP, XingZ, PengJ. Global asymptotic stability of CNNs with impulses and multi‐proportional delays. Mathematical Methods in the Applied Sciences2016; 39(4): 722-733. · Zbl 1338.34131
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