##
**Global exponential stability of cellular neural networks with time-varying coefficients and delays.**
*(English)*
Zbl 1068.68121

Summary: A class of cellular neural networks with time-varying coefficients and delays is considered. By constructing a suitable Lyapunov functional and utilizing the technique of matrix analysis, some new sufficient conditions on the global exponential stability of solutions are obtained. The results obtained in this paper improve and extend some of the previous results.

### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

### Keywords:

Global exponential stability; Lyapunov functional; Time-varying coefficient; Time-varying delay; Cellular neural network
PDFBibTeX
XMLCite

\textit{H. Jiang} and \textit{Z. Teng}, Neural Netw. 17, No. 10, 1415--1425 (2004; Zbl 1068.68121)

Full Text:
DOI

### References:

[1] | Arik, S., Stability analysis of delayed neural networks, IEEE Transactions on Circuits Systems I, 47, 1089-1092 (2000) · Zbl 0992.93080 |

[2] | Arik, S.; Tavsanoglu, V., On the global asymptotic stability of delay cellular neural networks, IEEE Transactions on Circuits Systems I, 47, 571-574 (2000) · Zbl 0997.90095 |

[3] | Burton, T. A., Stability and periodic solutions of ordinary and functional differential equations (1985), Academic Press: Academic Press New York · Zbl 0635.34001 |

[4] | Cao, J., Periodic solutions and exponential stability in delayed cellular neural networks, Physical Review E, 60, 3, 3244-3248 (1999) |

[5] | Cao, J., Periodic oscillation and exponential stability of delayed CNNs, Physics Letters A, 270, 157-163 (2000) |

[6] | Cao, J., Global exponential stability and periodic solutions of delayed cellular neural networks, Journal Comp. Syst. Sci, 60, 38-46 (2000) · Zbl 0988.37015 |

[7] | Cao, J., Global stability conditions for delayed CNNs, IEEE Transactions on Circuits Systems I, 48, 1330-1333 (2001) · Zbl 1006.34070 |

[8] | Cao, J.; Wang, L., Exponential stability and periodic oscillator solution in BAM networks with delays, IEEE Transactions on Neural Networks, 13, 457-463 (2002) |

[9] | Cao, J.; Wang, J., Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE Transactions on Circuits Systems I, 50, 34-44 (2003) · Zbl 1368.34084 |

[10] | Chen, A.; Cao, J., Existence and attractitivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients, Applied Mathematics and Computation, 134, 125-140 (2003) · Zbl 1035.34080 |

[11] | Chen, A.; Huang, L.; Cao, J., Existence and stability of almost periodic solution for BAM neural networks with delays, Applied Mathematics and Computation, 137, 177-193 (2003) · Zbl 1034.34087 |

[12] | Chu, T., An exponential convergence estimate for analog neural networks with delay, Physics Letters A, 283, 113-118 (2001) · Zbl 0977.68071 |

[13] | Dong, Q.; Matsui, K.; Huang, X., Existence and stability of periodic solutions for Hopfield neural network equations with periodic input, Nonlinear Analysis, 49, 471-479 (2002) · Zbl 1004.34065 |

[14] | Huang, H.; Cao, J.; Wang, J., Global exponential stability and periodic solutions of recurrent neural networks with delays, Physics Letters A, 298, 393-404 (2002) · Zbl 0995.92007 |

[15] | Jiang, H.; Li, Z.; Teng, Z., Boundedness and stability for nonautonomous cellular neural networks with delay, Physics Letters A, 306, 313-325 (2003) · Zbl 1006.68059 |

[16] | Jiang, H.; Teng, Z., Boundedness and stability for nonautonomous cellular neural networks with delay, Applied Mathematical and Mechanics (2003), in press · Zbl 1006.68059 |

[17] | Liang, J.; Cao, J., Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays, Physics Letters A, 318, 53-64 (2003) · Zbl 1037.82036 |

[18] | Lu, H., Stability criteria for delayed neural networks, Physical Review E, 64, 1-13 (2001), 051901 |

[19] | Mohamad, S., Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Physica D, 159, 233-251 (2001) · Zbl 0984.92502 |

[20] | Mohamad, S.; Gopalsamy, K., Dynamics of a class of discrete-time neural networks and their continuous-time counterparts, Mathematics and Computers in Simulation, 53, 1-39 (2000) |

[21] | Peng, J.; Qiao, H.; Xu, Z., A new approach to stability of neural networks with time-varying delays, Neural Networks, 15, 95-103 (2002) |

[22] | Shayer, L. P.; Campbell, S. A., Stability, bifurcation, and multistability in a system of two coupled neural with multiple time delays, SIAM Journal of Applied Mathematics, 61, 673-700 (2000) · Zbl 0992.92013 |

[23] | Takahashi, N., A new sufficient condition for complete stability of cellular neural networks with delay, IEEE Transactions on Circuits Systems I, 47, 6, 791-799 (2000) |

[24] | Van Den Driessche, P.; Zou, X., Global attractivity in delayed Hopfield neural network models, SIAM Journal of Applied Mathematics, 58, 1878-1890 (1998) · Zbl 0917.34036 |

[25] | Wei, J.; Ruan, S., Stability and bifurcation in a neural network model with two delays, Physica D, 130, 255-272 (1999) · Zbl 1066.34511 |

[26] | Zhang, J.; Jin, X., Global stability analysis in delay Hopfield neural network models, Neural Networks, 13, 745-753 (2000) |

[27] | Zhang, Y.; Pheng, A. H.; Kwong, S. L., Convergence analysis of cellular neural networks with unbounded delay, IEEE Transactions on Circuits Systems I, 48, 6, 680-687 (2001) · Zbl 0994.82068 |

[28] | Zhou, D.; Cao, J., Global exponential stability conditions for cellular neural networks with time-varying delays, Applied Mathematics and Computation, 131, 487-496 (2002) · Zbl 1034.34093 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.