## 1 Introduction
Moreover, the sampled-data communication mechanism requires higher communication rates to satisfy the worst possible extreme situations, which would increase the burden of networks and cause time delay or packet loss. According to [15], the event-triggered communication mechanism was proposed for microgrid secondary control to realize need-based data exchanges while meeting the performance requirements. A similar event-triggered control strategy was also applied in [16]. However, it is noteworthy that event-triggered communication requires continuous monitoring of the state variables of agents, which would place a heavy computation burden on each DG local controller. Moreover, the objectives of the abovementioned event-triggered method are only to synchronize the output voltages of DGs to their nominal values or realize reactive power sharing without considering voltage restoration. To the author's knowledge, the secondary control for average voltage restoration while maintaining reactive powering sharing using an appropriate event-triggered communication mechanism has not been discussed. While the communication network facilitates distributed control strategies, it leads to the vulnerability of microgrids to malicious cyber attacks. In general, cyber attacks can be categorized into: denial-of-service (DoS) attacks and deception attacks. Deception attack, such as false data attack (FDIA) and replay attack, is to compromise the integrity of measurements or transmitted data packets, while DoS attack is to block legitimate data transmissions or interfere with receptions. In the research field of the DoS attacks' detection mechanism, a collaborative real-time intrusion detection approach based on blockchain combined with SVM was developed in [17]. In [18], a signal temporal logic (STL)-based attack detection strategy was presented that can detect both FDIA and DoS attacks for microgrids. In the aspect of the DoS attack-resilient secondary control scheme, a software-defined microgrid control architecture was designed for resilience against DoS attacks in [19]. A finite-time control strategy was proposed for a battery energy storage system under DoS attacks in [20], but a communication recovery mechanism must be added to ensure the robustness of the method. In [21], an event-triggered control strategy was proposed for voltage restoration of a microgrid subject to DoS attacks, but this method requires the system to meet exponential stability conditions, which limits its application range. In [22], the intermittent DoS attacks were modeled as time delay and the impact of attacks on microgrid stability was analyzed, but no mitigation measures were proposed. In [23], a resilient control scheme with the power talk mechanism was established which can detect DoS attacks through adjusting droop coefficients, but this method is sensitive to load changes. Due to the fact that no communication networks are required, a decentralized control scheme has the natural advantages of resisting cyber attacks. However, it is noteworthy that the secondary control with no communication networks is still an open research field and the main challenges are related to modeling, stability, and robustness [24]. Since distributed structures have been widely studied and applied in engineering, it is of significance to propose a distributed resilient secondary control strategy to ensure voltage restoration and reactive power sharing under DoS attacks, which motivate our research. In this paper, we focus on the distributed secondary control for average voltage restoration and reactive power sharing of an islanded microgrid by taking into account the communication burden and the impact of DoS attacks. The communication mechanism of a distributed secondary controller is changed from the traditional periodic sampling manner to a new self-triggered manner in which continuous monitoring of neighboring DG's state can be avoided.