In this study, the problem of noise-input-to-state stability for switching stochastic nonlinear systems with impulses is investigated. There are two outstanding features of the investigated systems: (a) the occurrences of swithcings and impulses are allowed to be asynchronous; (b) the impulsive maps not only depend on the subsystems but also are different for the different impulsive instants. The noise-input-to-state stability problem is first considered for systems, where switching instants and impulsive intervals are confined by the mode-dependent average dwell time and impulsive interval, respectively. Then, we revisit the noise-input-to-state stability for nonlinear systems with stochastic switching and impulsive densities. To derive less conservative sufficient conditions, multiple Lyapunov functions with the indefinite weak infinitesimal generator and some fundamental stochastic techniques are applied. A simulation example is proposed to illustrate the effectiveness of the provided criteria.

在这项研究中，研究了具有脉冲的随机非线性系统的噪声输入到状态稳定性问题。所研究的系统有两个突出的特点：（a）允许开关和脉冲的发生是异步的；(b) 脉冲图不仅取决于子系统，而且对于不同的脉冲时刻也不同。首先考虑系统的噪声输入到状态稳定性问题，其中切换瞬间和脉冲间隔分别受模式相关的平均停留时间和脉冲间隔限制。然后，我们重新审视了具有随机切换和脉冲密度的非线性系统的噪声输入到状态稳定性。为了推导出不太保守的充分条件，应用了具有不定弱无穷小生成器的多个 Lyapunov 函数和一些基本的随机技术。提出了一个模拟示例来说明所提供标准的有效性。