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**Dynamic analysis of Markovian jumping impulsive stochastic Cohen-Grossberg neural networks with discrete interval and distributed time-varying delays.**
*(English)*
Zbl 1194.93191

Summary: The dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen-Grossberg Neural Networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a Linear Matrix Inequality (LMI), which can be easily calculated by LMI Toolbox in MATLAB. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays known from the literature.

### MSC:

93D20 | Asymptotic stability in control theory |

60J75 | Jump processes (MSC2010) |

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

93E03 | Stochastic systems in control theory (general) |

15A39 | Linear inequalities of matrices |

### Keywords:

asymptotic stability; Cohen-Grossberg neural networks; linear matrix inequality; Lyapunov-Krasovskii functional; Markovian jumping parameters; impulsive stochastic neural networks
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\textit{R. Rakkiyappan} and \textit{P. Balasubramaniam}, Nonlinear Anal., Hybrid Syst. 3, No. 4, 408--417 (2009; Zbl 1194.93191)

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### References:

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