Security of Network Systems Under Cyber-Attack

From the existing literature, one knows that the system robustness and stability are fully considered under time delay (Li and Ren 2021; Xiao et al. 2018), model uncertainties (Meng 2019; Meng and Moore 2017), and system switching process (Xue et al. 2022), etc. In addition, network systems are ubiquitous in real life, and malicious cyber-attacks often occur in the cyberspace and signal transmission process. Malicious attacks might result in data dropout (Bu et al. 2013; Liu and Ruan 2017, 2018) and system failure (Li et al. 2015), etc. How can systems be kept stable and safe from various malicious attacks? This problem attracts attention to the secure control, and a number of security control protocols are proposed. For example, Wan et al. (2017) proposes a security control strategy based on observation and switching topology. In He et al. (2018), the impulsive control method is used to achieve the secure synchronization of systems. Further, the security problems of multiple cyber-attacks are studied by using the cooperative control scheme (Tahoun 2021) and PID control strategy (Zhao et al. 2021). These results provide effective control strategies for achieving system security. However, some sufficient conditions, such as conditions (16a) and (16b) in Ref. Zhao et al. (2021), are a little complicated and hard to check in the real application if the dimension of the model is big. In addition, the combination of multiple cyber-attacks increases the difficulty of the theoretical analysis. Hence, to achieve some simple security conditions of systems with multiple cyber-attacks, we try to find applicable approaches for analyzing and obtaining some concise conditions.