## 1 Introduction  
The research of distributed cooperation and coordination of MAS has received considerable attention in recent years due to the rapid development of computer science and the broad potential application prospects in various fields, such as cooperative surveillance [1], formation control of unmanned aerial vehicles [2], attitude synchronization of spacecrafts [3], swarm intelligence [4] and so on. The theoretical study of this problem involves many branches, including consensus, containment, synchronization and formation [5, 6, 7]. Formation control, as one of the critical problems in distributed cooperative control systems, aims to design control laws which could drive the states or outputs of all agents to reach a predefined configuration. In the past few decades, many classical approaches have been proposed to achieve formation control, such as leader-follower, virtual structure and behavior-based approaches. In [8], [PERSON] studied the leader-follower formation control for mobile robots and the input constraints were considered. The virtual structure method was used to realize formation control and obstacle avoidance for a group of wheeled mobile robots under severe disturbances and system uncertainties in [9]. In [10], [PERSON] proposed a decentralized behavior-based formation control algorithm and the function of obstacle avoidance was considered. Although the above three traditional methods have proved very effective to solve the formation problem, it must be pointed out that these three strategies have their own weaknesses. For example, if the leader-follower based method lacks robustness due to the failure of the explicit leader, this may destroy the whole formation tracking, and the virtual structure-based method is not fully distributed as it requires each object to track its own waypoints [11]. Over the past few years, great progress has been achieved in consensus control of MAS, and numerous results have been acquired [12; 13; 14]. In [15], [PERSON] extended the consensus algorithm for a second-order multi-agent system, and those algorithms were introduced to solve the formation problem. In the conclusion, [PERSON] pointed out that \"many existing methods, such as leader-follower, behavioral and virtual structure/virtual leader formation control approaches can be unified in the general framework of consensus building.\" More results on the formation control problem based on a consensus algorithm could be found in [16; 17; 18]. It should be pointed out that in [16; 17; 18], the formation controllers are both based on distributed static consensus protocol. In classical static consensus protocol, the designer should acquire the entire communication graph and compute the coupling weights between the neighbor agents. In other words, these consensus protocols cannot be computed and implemented by each agent in a fully distributed way. To address this limitation, [PERSON] [19] proposed an adaptive control method, which could be updated by the neighbor's information. In [20], [PERSON] modified the protocol by adding a monotone increasing subitem to study the MAS's consensus problem with a directed communication graph. Not only for general linear systems, but for uncertain systems [21], nonlinear systems [22] and higher-order systems [23]; all of the above topics were addressed by previous researchers. In practical application, the communication connection between agents will be affected by the environment and fault. When the working condition is poor or the agent fails, the communication signal may be interrupted. The addition of new agents will also cause a change in the connection relationship. When the communication topology changes over time, this makes the MAS more difficult to control. In the cooperative control of MAS, a very important problem is how to design the control protocol to drive the agents' synchronization based on the neighborhood information, in case of communication interruption, reconnection and communication delay.