Consensus for discrete-time multi-agent systems without the precise model of packet dropouts

In this paper, we investigate the consensus problem for discrete-time linear multi-agent systems (MASs) with an imprecise packet dropout model. The precise packet dropout model, such as dropout patterns and packet dropout rate, is not available sometimes, since the strategy of malicious attackers is difficult to be known as a prior. To model packet dropouts accurately, our method concentrates on the proportion of time that packet dropouts and packets received being excited during a long run. Besides, both the upper and lower bound of packet dropouts are employed to represent the failure rate and recovery rate in the presence of attackers. First, we transform the consensus problem of multi-agent systems into the stability of a multi-mode switching system by the decomposition method. Then, the evolution of equivalent system states is analyzed by varying the system step size. Finally, based on the relationship between the dynamics of agent systems, upper and lower bounds of packet loss rates, and communication topology, a sufficient condition of consensus-ability for linear multi-agent systems with imprecise packet dropouts model is obtained and the conservation of the obtained packet loss rate decreases with an increase in time step. The theoretical results are tested by simulation examples.