## 1 Introduction  
With the rapid development of artificial intelligence and other technologies, cyber-physical systems (CPSs) that can highly integrate computation, communication, and control have emerged and been widely used in critical infrastructures, such as smart grids [1], intelligent transportation [2], industrial internet [3], and so on. In essence, CPSs are a class of complex networked control systems with a cyclic feedback mechanism, and the ubiquitous interconnection features make the openness increasingly enhanced [4]. This means that the deep interaction between the information world and physical plant has achieved global autonomy and collaboration. However, the influence of cyber security threats and physical safety issues has brought great challenges to the integrated protection of CPSs. Once the security defense mechanism deployed on the information layer fails, malicious adversaries can covertly invade the information systems, causing CPS-induced failures to spread rapidly in the communication media, thereby making the serious non-contact damage to the physical process. Since physical systems operate in a relatively isolated environment, there is a lack of in-depth understanding of external network threats and internal security vulnerabilities [5]. Thus, it is of great value to design advanced security control strategies to ensure the safe operation of plants in an unreliable network environment. Recently, security issues for CPSs have attracted widespread attention, such as intrusion identification [6; 7; 8], secure state estimation [9; 10; 11], stability analysis [12; 13; 14; 15], and resilient control [16; 17; 18; 19]. In CPSs, malicious attackers have developed various remote intrusion modes by destroying the security requirements of physical systems, such as denial-of-service (DoS) attacks, false data injection (FDI) attacks, and deception attacks [20], where DoS attacks force system service interruption by occupying the limited communication bandwidth. In addition, DoS attacks do not need to acquire any prior system knowledge, which implies that DoS attacks can be easily launched without regard for privacy protection [21]. In this attack scenario, the abnormal behaviors caused by DoS attacks can be quickly perceived. However, the access to control and measurement signals will be lost, making it impossible to effectively deal with this attack behavior. Thus, it is necessary to develop an advanced security control strategy with robustness and intrusion tolerance to ensure that CPSs can operate smoothly in a degraded manner under DoS attacks. The authors in [12] have proposed the concept of _\"resilient control\"_ to characterize the basic ability of CPSs to defend against DoS attacks. In [13], the authors developed an observer-based security control strategy for linear CPSs with multiple parallel transmission channels. The maximum operational duty cycle tolerated by CPSs under DoS attacks was obtained. To ensure both steady-state accuracy and transient security, the authors in [22] designed an active security control policy, where DoS attacks are assumed to occur in both control and measurement channels. The relationship between the resilience and communication bandwidth was studied in [23], where the bit rate condition under DoS attacks depends on the attack parameters and system matrices. The issue of secure consensus for interconnected CPSs under DoS attacks was discussed in [24; 25; 26; 27; 28], where the authors in [25] developed a time-varying resilient control scheme to ensure the secure consensus of the agent team. In [28], the authors discussed the co-design of the fault detection algorithm and consensus control protocol for interconnected CPSs under hidden DoS attacks. Since CPSs are susceptible to environmental mutations or random failures of physical components, they may consist of multiple subsystems with different structures and parameters.