Consensus of discrete-time multi-agent systems with nonlinear local rules and time-varying delays

In a multi-agent system (MAS), the agents are often considered to be autonomous entities, such as robots or software programs, each under the influence of a local rule, representing its interaction with other agents. Over the past few years, most research in the study of discrete-time MAS´s concentrates on linear local rules. However, local interactions between agents are more likely to be governed by nonlinear rules with time-varying delays. This paper investigates the consensus of discrete-time MAS´s with nonlinear local rules and time-varying delays. Based on a representative model, we obtain some basic criteria for the consensus of such MAS´s. These results cover several existing results as special cases. Moreover, the above criteria are applied to the consensus of the classical Vicsek model with time-varying delays. Simulation results are presented to validate the obtained criteria.