Abstract This paper is concerned with the resilient filtering problem for a class of discrete-time stochastic nonlinear systems with both time-varying delays and probabilistic distributed delays. In order to save the limited communication resource, stochastic communication protocols (SCPs) with multiple rules governed by a switching signal are employed to schedule the data transmission between the sensors and the filter for complying with different network scenarios and preserving the desired performance. An approach based on average dwell time (ADT) is utilized to establish the rule of SCPs for different scenarios. The purpose of the filtering problem is to design a resilient filter such that, under the regulation of SCPs, the dynamics of the filtering error is exponentially mean-square stable, and satisfies a prescribed disturbance attenuation level in a l 2 - l ∞ sense. A sufficient condition for the exponential mean-square stability is first derived and the l 2 - l ∞ performance is then guaranteed. In terms of certain linear matrix inequalities, the solvability of the addressed problem is discussed and the explicit expression of the desired resilient filter is also parameterized. Finally, a numerical example is provided to demonstrate the validity of the proposed design approach.

中文翻译：

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基于停留时间的通信调度的弹性ℓ2-ℓ∞过滤

摘要 本文研究一类具有时变时滞和概率分布时滞的离散时间随机非线性系统的弹性滤波问题。为了节省有限的通信资源，采用由开关信号控制的具有多个规则的随机通信协议（SCP）来调度传感器和过滤器之间的数据传输，以适应不同的网络场景并保持所需的性能。使用基于平均停留时间 (ADT) 的方法来建立针对不同场景的 SCP 规则。滤波问题的目的是设计一个弹性滤波器，使得在 SCP 的调节下，滤波误差的动态是指数均方稳定的，并且在 al 2 - l ∞ 意义上满足规定的干扰衰减水平。首先推导出指数均方稳定性的充分条件，然后保证 l 2 - l ∞ 性能。就某些线性矩阵不等式而言，讨论了所解决问题的可解性，并且还参数化了所需弹性滤波器的显式表达式。最后，提供了一个数值例子来证明所提出的设计方法的有效性。