具有通信时延的离散时间二阶多个体网络的一致性问题

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

针对具有通信时延的离散时间二阶多个体系统的一致性问题，采用了具有静态领导者的一致性算法．根据广义Nyquist判据和Gerschgorin圆盘定理，得到了系统渐近收敛到领导者状态的充分条件．在个体与领导者构成的连接拓扑满足一定连通性的前提下，该充分条件是分散形式的，与控制参数、邻居个体之间的连接权值相关，而与通信时延大小无关．仿真结果证明了结论的正确性．

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.