This article investigates event-triggered and self-triggered L∞\mathcal {L}_{\infty } control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve L∞\mathcal {L}_{\infty } performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

中文翻译：

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DoS 攻击下马尔可夫跳跃随机非线性系统的事件触发和自触发 L 鈭 控制


本文研究了遭受拒绝服务 (DoS) 攻击的马尔可夫跳跃随机非线性系统的事件触发和自触发 L∞\mathcal {L}_{\infty } 控制问题。当攻击阻止系统设备通过网络获取有效信息时，构建一个具有不稳定子系统的新交换模型来表征 DoS 攻击的效果。在切换模型的基础上，利用多重李亚普诺夫函数方法，并提供了一组结合事件触发方案（ETS）和DoS攻击限制的充分条件来保持L∞\mathcal {L}_{\infty } 表现。特别是考虑到基于数学期望的ETS难以在实际平台上实现，提出了一种无数学期望的自触发方案(STS)。同时，为了避免一般的外源干扰导致的Zeno行为，STS中预先固定了一个正的下界。另外，STS中设计了指数参数，以降低触发频率。基于STS，讨论了系统在没有外生扰动的情况下的均方渐近稳定性和几乎确定的指数稳定性。最后，给出两个例子来验证所提方法的有效性。