Improved approaches to stability criteria for neural networks with time-varying delays.

*(English)*Zbl 1287.93073Summary: In this paper, the problem of stability analysis for neural networks with time-varying delays is considered. By the use of a newly augmented Lyapunov functional and some novel techniques, sufficient conditions to guarantee the asymptotic stability of the concerned networks are established in terms of linear matrix inequalities (LMIs). Three numerical examples are given to show the improved stability region of the proposed works.

##### MSC:

93D20 | Asymptotic stability in control theory |

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

##### Keywords:

stability analysis; neural networks with time-varying delays; asymptotic stability; linear matrix inequalities (LMIs)
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\textit{O. M. Kwon} et al., J. Franklin Inst. 350, No. 9, 2710--2735 (2013; Zbl 1287.93073)

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##### References:

[1] | Chua, L. O.; Wang, L., Cellular neural networksapplications, IEEE Transactions on Circuits and Systems, 35, 1273-1290, (1988) |

[2] | Joya, G.; Atencia, M. A.; Sandoval, F., Hopfield neural networks for optimizationstudy of the different dynamics, Neurocomputing, 43, 219-237, (2002) · Zbl 1016.68076 |

[3] | Xu, S.; Lam, J.; Ho, D. W.C., Novel global robust stability criteria for interval neural networks with multiple time-varying delays, Physics Letters A, 342, 322-330, (2005) · Zbl 1222.93178 |

[4] | Liu, Y.; Wang, Z.; Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Networks, 19, 667-675, (2006) · Zbl 1102.68569 |

[5] | Ozcan, N.; Arik, S., A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays, Nonlinear Analysis: Real World Applications, 10, 3312-3320, (2009) · Zbl 1162.92005 |

[6] | Faydasicok, O.; Arik, S., Equilibrium and stability analysis of delayed neural networks under parameter uncertainties, Applied Mathematics and Computation, 218, 6716-6726, (2012) · Zbl 1245.34075 |

[7] | Faydasicok, O.; Arik, S., Further analysis of global robust stability of neural networks with multiple time delays, Journal of the Franklin Institute, 349, 813-825, (2012) · Zbl 1273.93124 |

[8] | Faydasicoka, O.; Arik, S., Robust stability analysis of a class of neural networks with discrete time delays, Neural Networks, 29-30, 2012, (2012) |

[9] | Xu, S.; Lam, J.; Ho, D. W.C.; Zou, Y., Delay-dependent exponential stability for a class of neural networks with time delays, Journal of Computational and Applied Mathematics, 183, 16-28, (2005) · Zbl 1097.34057 |

[10] | Xu, S.; Lam, J.; Ho, D. W.C.; Zou, Y., Novel global asymptotic stability criteria for delayed cellular neural networks, IEEE Transactions on Circuits and Systems Part II—Express Briefs, 52, 349-353, (2005) |

[11] | Zhang, B.; Xu, S.; Zou, Y., Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays, Neurocomputing, 72, 321-330, (2008) |

[12] | Kwon, O. M.; Park, J. H.; Lee, S. M., On robust stability for uncertain neural networks with interval time-varying delays, IET Control Theory & Applications, 2, 625-634, (2008) |

[13] | Balasubramaniam, P.; Lakshmanan, S., Delay-range dependent stability criteria for neural networks with Markovian jumping parameters, Nonlinear Analysis: Hybrid Systems, 3, 749-756, (2009) · Zbl 1175.93206 |

[14] | Balasubramaniam, P.; Lakshmanan, S.; Rakkiyappan, R., Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties, Neurocomputing, 72, 3675-3682, (2009) |

[15] | Li, T.; Guo, L.; Wu, L.; Sun, C., Delay-dependent robust stability criteria for delay neural networks with linear fractional uncertainties, International Journal of Control, Automation, and Systems, 7, 281-287, (2009) |

[16] | Li, T.; Zheng, W. X.; Lin, C., Delay-slope-dependent stability results of recurrent neural networks, IEEE Transactions on Neural Networks, 22, 2138-2143, (2011) |

[17] | Zhang, Y.; Yue, D.; Tian, E., New stability criteria of neural networks with interval time-varying delaysa piecewise delay method, Applied Mathematics and Computation, 208, 249-259, (2009) · Zbl 1171.34048 |

[18] | Kwon, O. M.; Park, Ju H., Improved delay-dependent stability criterion for neural networks with time-varying delays, Physics Letters A, 373, 529-535, (2009) · Zbl 1227.34030 |

[19] | Xiao, S.-P.; Zhang, X.-M., New globally asymptotic stability criteria for delayed neural networks, IEEE Transactions on Circuits and Systems Part II—Express Briefs, 56, 659-663, (2009) |

[20] | Mou, S.; Gao, H.; Lam, J.; Qiang, W., A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay, IEEE Transactions on Neural Networks, 19, 532-535, (2008) |

[21] | Zhang, H.; Liu, Z.; Hung, G.-B.; Wang, Z., Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay, IEEE Transactions on Neural Networks, 21, 91-106, (2010) |

[22] | Li, T.; Song, A.; Fei, S.; Wang, T., Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay, IEEE Transactions on Neural Networks, 21, 1365-1371, (2010) |

[23] | Tian, J.; Xie, X., New asymptotic stability criteria for neural networks with time-varying delay, Physics Letters A, 374, 938-943, (2010) · Zbl 1235.92007 |

[24] | Li, T.; Song, A.; Xue, M.; Zhang, H., Stability analysis on delayed neural networks based on an improved delay-partitioning approach, Journal of Computational and Applied Mathematics, 235, 3086-3095, (2011) · Zbl 1207.92002 |

[25] | Tian, J.; Zhong, S., Improved delay-dependent stability criterion for neural networks with time-varying delay, Applied Mathematics and Computation, 217, 10278-10288, (2011) · Zbl 1225.34080 |

[26] | Zeng, H.-B.; He, Y.; Wu, M.; Zhang, C.-F., Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays, IEEE Transactions on Neural Networks, 22, 806-812, (2011) |

[27] | Wang, Y.; Yang, C.; Zuo, Z., On exponential stability analysis for neural networks with time-varying delays and general activation functions, Communications in Nonlinear Science and Numerical Simulation, 17, 1447-1459, (2012) · Zbl 1239.92005 |

[28] | Kwon, O. M.; Lee, S. M.; Park, Ju H.; Cha, E. J., New approaches on stability criteria for neural networks with interval time-varying delays, Applied Mathematics and Computation, 218, 9953-9964, (2012) · Zbl 1253.34066 |

[29] | Kwon, O. M.; Park, Ju H.; Lee, S. M.; Cha, E. J., Analysis on delay-dependent stability for neural networks with time-varying delays, Neurocomputing, 103, 114-120, (2013) |

[30] | Gu, K., A further refinement of discretized Lyapunov functional method for the stability of time-delay systems, International Journal of Control, 74, 967-976, (2001) · Zbl 1015.93053 |

[31] | Ariba, Y.; Gouaisbaut, F., An augmented model for robust stability analysis of time-varying delay systems, International Journal of Control, 82, 1616-1626, (2009) · Zbl 1190.93076 |

[32] | Kim, S. H.; Park, P.; Jeong, C., Robust \(H_\infty\) stabilisation of networked control systems with packet analyser, IET Control Theory & Applications, 4, 1828-1837, (2010) |

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

[34] | K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of the IEEE Conference on Decision and Control, Sydney, Australia, December 2000, pp. 2805-2810. |

[35] | Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004 |

[36] | Skelton, R. E.; Iwasaki, T.; Grigoradis, K. M., A unified algebraic approach to linear control design, (1997), Taylor & Francis New York |

[37] | Song, Q.; Cao, J., Passivity of uncertain neural networks with both leakage delay and time-varying delay, Nonlinear Dynamics, 67, 1695-1707, (2012) · Zbl 1242.92005 |

[38] | Song, Q., Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling, Applied Mathematics and Computation, 216, 1605-1613, (2010) · Zbl 1194.34145 |

[39] | Song, Q., Synchronization analysis of coupled connected neural networks with mixed time delays, Neurocomputing, 72, 3907-3914, (2009) |

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