Further results on exponential stability of neural networks with time-varying delay.

*(English)*Zbl 1338.92020Summary: We investigate the problem of the exponential stability for a class of neural networks with time-varying delay. A triple integral term and a term considering the delay information in a new way are introduced to the Lyapunov-Krasovskii functional (LKF). The obtained criterion show advantages over the existing ones since not only a novel LKF is constructed but also several techniques such as Wirtinger-based inequality and convex combination technique are used to estimate the upper bound of the derivative of the LKF. Finally, a numerical example is provided to verify the effectiveness and benefit of the proposed criterion.

##### MSC:

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{M.-D. Ji} et al., Appl. Math. Comput. 256, 175--182 (2015; Zbl 1338.92020)

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##### References:

[1] | Chua, L.; Yang, L., Cellular neural networks: theory, IEEE Trans. Circuits Syst., 35, 10, 1257-1272, (1988) · Zbl 0663.94022 |

[2] | Chua, L.; Roska, T., Cellular neural networks and visual computing, (2002), Cambridge Univ. Press Cambridge, U.K. |

[3] | Hua, C. C.; Yang, X.; Yan, J.; Guan, X. P., New exponential stability criteria for neural networks with time-varying delays, IEEE Trans. Circuits Syst. II, 58, 12, 913-935, (2011) |

[4] | Wu, Z. G.; Lam, J.; Su, H. Y.; Chu, J., Stability and dissipativity analysis of static neural networks with time delay, IEEE Trans. Neural Netw. Learn. Syst., 23, 2, 199-210, (2012) |

[5] | Ji, M. D.; He, Y.; Zhang, C. K.; Wu, M., Novel stability criteria for recurrent neural networks with time-varying delay, Neurocomputing, 138, 383-391, (Aug. 2014) |

[6] | Mou, S.; Gao, H.; Qiang, W.; Chen, K., New delay-dependent exponential stability for neural networks with time delay, IEEE Trans. Syst., Man, Cybern., B, Cybern., 38, 2, 571-576, (2008) |

[7] | Kwon, O. M.; Lee, S. M.; Park, J. H.; Cha, E. J., New approaches on stability criteria for neural networks with interval time-varying delays, Appl. Math. Comput., 218, 19, 9953-9964, (Jun. 2012) |

[8] | Lee, T. H.; Park, M. J.; Park, J. H.; Kwon, O. M.; Lee, S. M., Extended dissipative analysis for neural networks with time-varying delays, IEEE Trans. Neural Netw., Learn. Syst., 25, 10, 1936-1941, (2014) |

[9] | Zeng, H. B.; Park, J. H.; Shen, H., Robust passivity analysis of neural networks with discrete and distributed delays, Neurocomputing, 149, 1092-1097, (2015) |

[10] | Wang, Z.; Zhang, H.; Jiang, B., LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures, IEEE Trans. Neural Netw., 22, 7, 1032-1045, (Jul. 2011) |

[11] | Zhang, X. M.; Han, Q. L., Global asymptotic stability for a class of generalized neural networks with interval time-varying delays, IEEE Trans. Neural Netw., 22, 8, 1180-1192, (2011) |

[12] | Zhang, X. M.; Han, Q. L., New Lyapunov-krasovskii functionals for global asymptotic stability of delayed neural networks, IEEE Trans. Neural Netw., 20, 3, 533-539, (Mar. 2009) |

[13] | Kwon, O. M.; Park, M. J.; Lee, S. M.; Park, J. H.; Cha, E. J., Stability for neural networks with time-varying delays via some new approaches, IEEE Trans. Neural Netw., Learning Syst., 24, 2, 181-193, (2013) |

[14] | Kwon, O. M.; Park, M. J.; Park, J. H.; Lee, S. M.; Cha, E. J., On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov-krasovskii functional, Commun. Nonlinear Sci. Numer. Simul., 19, 9, 3184-3201, (2014) |

[15] | Zhang, C. K.; He, Y.; Jiang, L.; Wu, Q. H.; Wu, M., Delay-dependent stability criteria for generalized neural networks with two delay components, IEEE Trans. Neural Netw., Learn. Syst., 25, 7, 1263-1276, (2014) |

[16] | Liao, X. F.; Chen, G.; Sanchez, E. N., Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Netw., 15, 7, 855-866, (Sep. 2002) |

[17] | He, Y.; Wu, M.; She, J. H., Delay-dependent exponential stability of delayed neural networks with time-varying delay, IEEE Trans. Circuits Syst. II, Exp. Briefs, 53, 7, 553-557, (2006) |

[18] | Wu, M.; Liu, F.; Shi, P.; He, Y.; Yokoyama, R., Exponential stability analysis for neural networks with time-varying delay, IEEE Trans. Syst., Man, Cybern., B, Cybern., 38, 4, 1152-1156, (2008) |

[19] | Wang, Y.; Yang, C.; Zuo, Z., On exponential stability analysis for neural networks with time-varying delays and general activation functions, Commun. Nonlinear Sci. Numer. Simul., 17, 3, 1447-1459, (2012) · Zbl 1239.92005 |

[20] | Zheng, C. D.; Zhang, H.; Wang, Z., New delay-dependent global exponential stability criteria for cellular-type neural networks with time-varying delays, IEEE Trans. Circuits Syst. II, Exp. Briefs, 56, 3, 250-254, (2009) |

[21] | Zheng, C. D.; Zhang, H.; Wang, Z., Novel exponential stability criteria of high-order neural networks with time-varying delays, IEEE Trans. Syst., Man, Cybern., B, Cybern., 41, 2, 486-496, (2011) |

[22] | Wang, Z.; Zhang, H.; Li, P., An LMI approach to stability analysis of reaction-diffusion Cohen-Grossberg neural networks concerning Dirichlet boundary conditions and distributed delays, IEEE Trans. Syst., Man, Cybern., B, Cybern., 40, 6, 1596-1606, (2010) |

[23] | M.D. Ji, Y. He, M. Wu, C.K. Zhang, New exponential stability criterion for neural networks with time-varying delay, in: Proceeding of the 33rd Chinese Control Conference, 2014, Nanjing, China. |

[24] | Sun, J.; Liu, G. P.; Chen, J.; Reesb, D., Improved delay-range-dependent stability criteria for linear systems with time-varying delays, Automatica, 46, 2, 157-166, (2010) |

[25] | Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49, 9, 2860-2866, (Sep. 2013) |

[26] | Park, P.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238, (2011) · Zbl 1209.93076 |

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