In this paper, the finite-time memory fault detection filter (MFDF) is designed for nonlinear discrete systems with randomly occurring deception attacks, where the phenomenon of the randomly occurring deception attacks is characterised by a Bernoulli distributed random variable with known probability. To be specific, the finite-horizon data are employed to construct the MFDF. The main purpose of this paper is to design the MFDF such that, for all nonlinearities, external disturbances and randomly occurring deception attacks, the resultant augmented system is finite-time stable and attains the $H_{\mathrm{\infty }}$ performance. Accordingly, some sufficient conditions are developed to guarantee the existence of the desired fault detection filter parameters, where the solvability of the addressed problem is verified by the feasibility of certain matrix inequalities. Moreover, in order to show that the MFDF has better detection performance, a non-memory fault detection filter (NMFDF) is constructed to compare with the MFDF. Finally, two numerical simulations are utilised to illustrate the effectiveness of the proposed fault detection strategies and explain the superiority of the proposed MFDF.

本文针对具有随机发生的欺骗攻击的非线性离散系统设计了有限时间记忆故障检测滤波器（MFDF），其中随机发生的欺骗攻击的现象以具有已知概率的伯努利分布随机变量为特征。具体而言，采用有限水平数据构造MFDF。本文的主要目的是设计MFDF，使得对于所有非线性，外部干扰和随机发生的欺骗攻击，所得的增强系统是有限时间稳定的，并且能够达到$H_{\mathrm{\infty }}$性能。因此，开发了一些足够的条件来保证所需故障检测滤波器参数的存在，其中所解决问题的可解决性通过某些矩阵不等式的可行性得到验证。此外，为了表明MFDF具有更好的检测性能，构造了一个非内存故障检测滤波器（NMFDF）与MFDF进行比较。最后，利用两个数值模拟来说明所提出的故障检测策略的有效性并解释所提出的MFDF的优越性。