Global Asymptotic Stability Conditions of Delayed Neural Networks

ZHOU Dong-ming; CAO Jin-de; ZHANG Li-ming

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ZHOU Dong-ming, CAO Jin-de, ZHANG Li-ming. Global Asymptotic Stability Conditions of Delayed Neural Networks[J]. Applied Mathematics and Mechanics, 2005, 26(3): 341-348.

Citation:

ZHOU Dong-ming, CAO Jin-de, ZHANG Li-ming. Global Asymptotic Stability Conditions of Delayed Neural Networks[J]. Applied Mathematics and Mechanics, 2005, 26(3): 341-348.

Citation:

ZHOU Dong-ming, CAO Jin-de, ZHANG Li-ming. Global Asymptotic Stability Conditions of Delayed Neural Networks[J]. Applied Mathematics and Mechanics, 2005, 26(3): 341-348.

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Global Asymptotic Stability Conditions of Delayed Neural Networks

Department of Electronic Engineering, Fudan University, Shanghai 200433, P. R. China;
Department of Applied Mathematics, Southeast University, Nanjing 210096, P. R. China;

Received Date: 2003-04-28
Rev Recd Date: 2004-09-15
Publish Date: 2005-03-15

Abstract

Abstract

Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore, the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.
- cellular neural network,
- global stability,
- inequality of matrix,
- delay

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References(17)

References

[1]	Civalleri P P, Gilli L M, Pabdolfi L. On tability of cellular neural networks with delay[J].IEEE Trans Circuits Syst I,1993,40(3):157—165. doi: 10.1109/81.222796
[2]	Roska T, Wu C W, Chua L O. Stability of cellular neural networks with dominant nonlinear and delay-type template[J].IEEE Trans Circuits Syst I,1993,40(4):270—272. doi: 10.1109/81.224300
[3]	Arik S, Tavsanoglu V. On the global asymptotic stability of delayed cellular neural networks[J].IEEE Trans Circuits Syst I,2000,47(4):571—574. doi: 10.1109/81.841859
[4]	Arik S, Tavsanoglu V. Equilibrium analysis of delayed CNNs[J].IEEE Trans Circuits Syst I,1998,45(2):168—171. doi: 10.1109/81.661684
[5]	CAO Jin-de, ZHOU Dong-ming. Stability analysis of delayed cellular neural networks[J].Neural Networks,1998,11(9):1601—1605. doi: 10.1016/S0893-6080(98)00080-X
[6]	Feng C H, Plamondon R. On the stability analysis of delayed neural networks systems[J].Neural Networks,2001,14(9):1181—1188. doi: 10.1016/S0893-6080(01)00088-0
[7]	CAO Jin-de. On stability of delayed cellular neural networks[J].Physics Letters A,1999,261(5-6):303—308. doi: 10.1016/S0375-9601(99)00552-6
[8]	CAO Jin-de. A set of stability criteria for delayed cellular neural networks[J].IEEE Trans Circuits Syst I, 2001,48(4):494—498. doi: 10.1109/81.917987
[9]	Arik S. An improved global stability result for delayed cellular neural networks[J].IEEE Trans Circuits Systems I,2002,49(8):1211—1214. doi: 10.1109/TCSI.2002.801264
[10]	Liao T L, Wang F C. Global stability for cellular neural networks with time delay[J].IEEE Trans Neural Networks, 2000,11(6):1481—1484. doi: 10.1109/72.883480
[11]	CAO Jin-de. Global stability conditions for delayed CNNs[J].IEEE Trans Circuits Syst I, 2001,48(11):1330—1333. doi: 10.1109/81.964422
[12]	Zhang Y, Yu J B, Wu Y. Global stability analysis on a class of cellular neural networks[J].Science in China (Series E),2001,44(1):1—11.
[13]	CAO Jin-de, Wang L. Exponential stability and periodic oscillatory solution in BAM networks with delays[J].IEEE Trans Neural Networks,2002,13(2):457—463. doi: 10.1109/72.991431
[14]	CAO Jin-de. Exponential stability and periodic solutions of delayed cellular neural networks[J].Science in China (series E),2000,43(3):328—336.
[15]	Huang H,CAO Jin-de, Wang J. Global exponential stability and periodic solutions of recurrent neural networks with delays[J].Physics Letters A,2002,298(5-6):393—404. doi: 10.1016/S0375-9601(02)00537-6
[16]	CAO Jin-de. New results concerning exponential stability and periodic solutions of delayed cellular neural networks[J].Physics Letters A,2003,307(2-3):136—147. doi: 10.1016/S0375-9601(02)01720-6
[17]	CAO Jin-de,Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays[J].IEEE Trans Circuits Syst I,2003,50(1):34—44. doi: 10.1109/TCSI.2002.807494