This paper considers the problems on the mean square exponential synchronization and the almost surely exponential synchronization for neutral stochastic dynamical delay networks with Markovian switching via the single pinning impulsive control. By using a unified approach incorporating the concept of average impulsive interval and Lyapunov function, and the Borel–Cantelli lemma, two criteria on the mean square exponential stability and the almost surely exponential stability for impulsive neutral stochastic delay systems with Markovian switching are derived. It is shown that the impulsive control with a suitable impulsive strength can stochastically stabilize the underlying systems. With the symmetry and irreducibility of the switching topologies, and the obtained stochastic stability criteria, sufficient conditions are derived to determine the mean square exponential synchronization of the underlaying networks via the single pinning impulsive controller, which are given with algebraic inequalities and ${\mathcal {M}}$ -matrix. The almost surely exponential synchronization is also analyzed. Two examples are given to verify the validity of the theoretic results presented.

中文翻译：

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基于单钉住脉冲策略的中性随机延迟马尔可夫网络同步控制

本文考虑了通过单钉扎脉冲控制进行马尔可夫切换的中性随机动态延迟网络的均方指数同步和几乎肯定指数同步问题。通过使用包含平均脉冲间隔和李雅普诺夫函数的概念以及 Borel-Cantelli 引理的统一方法，推导出关于具有马尔可夫切换的脉冲中性随机延迟系统的均方指数稳定性和几乎肯定指数稳定性的两个标准。结果表明，具有合适脉冲强度的脉冲控制可以随机稳定底层系统。利用开关拓扑的对称性和不可约性，以及获得的随机稳定性准则，通过单钉扎脉冲控制器推导出充分条件来确定底层网络的均方指数同步，其由代数不等式和 ${\mathcal {M}}$ -matrix 给出。几乎可以肯定的指数同步也被分析。给出了两个例子来验证所提出的理论结果的有效性。