Consensus control and initialization region optimization for leader‐following multi‐agent systems under time‐varying communication delay and consecutive packet dropouts

This article is to investigate the consensus control and initialization region optimization for leader‐following multi‐agent systems with time‐varying communication delay and nonidentical consecutive packet dropouts. By combining the Bernoulli distribution model of the data loss and the Hadamard product, the control protocols affected by both communication delay and packet dropouts are utilized to formulate the consensus problem into the mean‐square stability problem of the augmented error systems. Resorting to the Lyapunov function methodology and a structure separation method, a sufficient condition to ensure the consensus is built in the form of linear matrix inequality. Relying on the given Lyapunov function and set‐membership analysis, an optimization procedure is proposed to simultaneously ensure the consensus and enlarge the estimated ellipsoid of initial conditions. The validity of the provided method is illustrated through a comparative simulation.