## 1 Introduction  
In recent years, many studies have been performed on distributed multi-agent systems (MASs) [1; 2; 3; 4; 5]. Among which, data sharing is regarded as a general scheme in terms of distributed MASs problems [6; 7]. In particular, communication costs play a crucial role in determining the number of messages send or receive by agents. Note that the commonly used continuous-time communication scheme was built on the assumption of sufficiently large communication bandwidth. However, from a practical point of view, it is not desirable. Concerning this problem, a discrete-time communication scheme was proposed based on periodic information exchange synchronously or asynchronously among agents [8]. Nevertheless, considering the increasing number of agents and the robustness requirements against internal uncertainties and external disturbances, it is unnecessary to exchange information and update the control actions for all agents simultaneously. As a particular sampling strategy, event-triggered control is an alternative to periodic sample control methods [9; 10; 11; 12; 13]. The distinct character of event-triggered control is that to achieve the desired task with a certain level of performance, control actions update only when a specific event occurs, and as a result, the trade-offs are mitigated between communication, computation, and actuator effort. Currently, event-triggered control has been studied extensively in distributed MASs [14; 15], centralized MASs [16; 17], as well as in many other MASs' cases. Moreover, event-triggered control hasalready been proven superior to the periodic sample control methods. It is also shown particularly useful in MASs' applications, such as consensus problems [10; 11], formation control [12; 13], collision avoidance [18], and tracking control [19; 20; 21]. However, for event-triggered conditions in MASs [22; 23], it still remains a challenge to exclude Zeno behavior, i.e., the system generates an infinite number of samplings over a finite time interval. Specifically, a sufficient condition to rule out Zeno behavior is to ensure that the event-triggered interval is strictly positive lower bounded [24; 25]. Different from consensus-type algorithms coupling with event-triggered control, in this paper, the attention is paid to the circle formation control problem for MASs, aiming at guiding multiple agents to form and maintain a predetermined geometry. The work in [26] is regarded as the original work, in which the continuous-time control protocol was designed to address the distributed circle formation problem. In [12], protocols combined with state-dependent event-triggered was proposed to solve the circle formation problem for first-order MASs, the framework of which enables the event-triggered condition to rule out Zeno behavior automatically. In [27], encoder-decoder strategies were used to achieve circle formation asymptotically with a finite-level uniform quantization, where the quantizer is not saturated in bounded communication as the number of agents increases. Moreover, based on [27], in order to address the problem circle formation problem for MASs with a limitation of communication, [13] investigated an innovative algorithm that relies on the combination of quantitative communication techniques and event-triggered control. In this paper, we mainly focus on the pull-based distributed event-triggered circle formation control for MASs over a class of weight-unbalanced digraphs. In our work, all agents, similar to the Pioneer 3-DX in [28], are equipped with a sensor to perceive the distances from themselves to the nearest neighbors in a counterclockwise direction and the counterparts in the clockwise direction. At event-triggered instants, one agent updates its controller when broadcasting its states to all its out-neighbors immediately. However, this does not indicate that the agent has to send a request to its in-neighbors at the event-triggered instance to ask for the state information.