This paper discusses the sampled-data input-to-state stabilization for delayed semi-Markovian jump neural networks subject to external disturbance. First, a hybrid closed-loop system is formulated, which contains continuous-time state signal, disturbance input signal, discrete-time control signal, and jumping parameters of the semi-Markovian process. Then, two time-dependent and mode-dependent Lyapunov functionals are constructed corresponding to different assumptions about the activation functions. Subsequently, two sufficient conditions concerning the sampled-data controller design are derived to ensure the mean-square input-to-state stability for the hybrid closed-loop system by utilizing the proposed Lyapunov functionals, a few inequalities, as well as some stochastic analysis techniques. It is worth remarking that the present conditions are capable of ensuring mean-square exponential stability of the closed-loop system in the absence of external disturbances. Lastly, a numerical example is employed to verify the validity of the proposed input-to-state stabilization methods.

本文讨论了受外部干扰影响的延迟半马尔可夫跳跃神经网络的采样数据输入状态稳定问题。首先，建立了一个混合闭环系统，包含连续时间状态信号、扰动输入信号、离散时间控制信号和半马尔可夫过程的跳跃参数。然后，对应于关于激活函数的不同假设，构造了两个时间相关和模式相关的 Lyapunov 泛函。随后，通过利用提出的 Lyapunov 泛函、一些不等式以及一些随机分析，导出了关于采样数据控制器设计的两个充分条件，以确保混合闭环系统的均方输入到状态稳定性技巧。值得注意的是，目前的条件能够保证闭环系统在没有外部干扰的情况下的均方指数稳定性。最后，通过一个数值例子来验证所提出的输入到状态稳定方法的有效性。