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This paper studies the leader-following consensus problem of discrete-time multi-agent systems with time-varying delays by developing a new cyclic switching scheme. First, two delay-dependent cycle dwell time switching laws are proposed for the first time. Second, by the proposed cyclic switching laws and constructed Lyapunov functionals, new leader-following consensus criteria for discrete-time multi-agent systems with time-varying delays are derived in the form of linear matrix inequalities. Compared with the existing literature, the developed cyclic switching method not only greatly improves the upper bound of time-varying delays in the multi-agent system, but also gives the estimation of upper and lower bounds for dwell time of the system. Finally, some simulations for the leader-following consensus of multi-agent systems with time-varying delays are presented to verify the feasibility of the proposed scheme.

New Results on Consensus of Multi-Agent Systems With Time-Varying Delays: A Cyclic Switching Technique