Consensus problem of discrete-time second-order multi-agent network with communication delay

The consensus algorithm with a static leader is proposed to solve the consensus problem of the discrete-time second-order multi-agent systems with communication delay. By the generalized Nyquist criterion and the Gerschgorin disc theorem, the sufficient conditions are obtained for the system to converge to the leader's states asymptotically. With the interconnection topology composed of the agents and the leader that satisfies certain connectivity conditions, the sufficient conditions are decentralized, dependent on the control parameters and the weights between the neighboring agents, and independent of the communication delay. Numerical examples are provided to illustrate the correctness of the results.