This paper focuses on the exponential stabilization problem for Markov jump neural networks with Time-varying Delays (TDs). Firstly, we provide a new Free-matrix-based Exponential-type Integral Inequality (FMEII) containing the information of attenuation exponent, which is helpful to reduce the conservativeness of stability criteria. To further save control cost, we introduce a sample-based Adaptive Event-triggered Impulsive Control (AEIC) scheme, in which the trigger threshold is adaptively varied with the sampled state. By fully considering the information about sampled state, TDs, and Markov jump parameters, a suitable Lyapunov–Krasovskii functional is constructed. With the virtue of FMEII and AEIC scheme, some novel stabilization criteria are presented in the form of linear matrix inequalities. At last, two numerical examples are given to show the validity of the obtained results.

中文翻译：

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时变时滞的自适应事件触发脉冲控制的马尔可夫跳跃神经网络的随机指数镇定

本文关注具有时变时滞（TDs）的Markov跳跃神经网络的指数稳定问题。首先，我们提供了一个新的基于自由矩阵的指数型积分不等式（FMEII），其中包含衰减指数信息，这有助于降低稳定性标准的保守性。为了进一步节省控制成本，我们引入了基于样本的自适应事件触发脉冲控制（AEIC）方案，其中触发阈值随采样状态而自适应地变化。通过充分考虑有关采样状态，TD和Markov跳变参数的信息，可以构建合适的Lyapunov–Krasovskii函数。借助FMEII和AEIC方案，以线性矩阵不等式的形式提出了一些新颖的稳定准则。最后，