Consensus Problem Of Multi-agent Systems With Time-delay Under Fixed Topology

Multi-agent system is a collection of agents.It solves large-scale complex problems through mutual communication and coordination between agents.It has strong robustness,reliability and high problem-solving efficiency.In recent years,multi-agent system has drawn much researchers' attentions due to its wide applications in satellite formation,mobile robot,unmanned aerial vehicle and other fields.In this paper,consensus problems are studied under continuous-time and discrete-time second-order multi-agent systems with time delay,respectively.Our main results and contributions are summarized as follows:1.The consensus problem of continuous-time second-order multi-agent systems is studied.By Hopf bifurcation theory,we obtain a sufficient condition to ensure that multi-agent systems can achieve consensus,and give the corresponding upper bound of time delay.2.The consensus problem of discrete-time second-order multi-agent systems under undirected topology is studied.By Jury criterion,we establish a sufficient and necessary consensus condition to ensure that multi-agent systems can achieve consensus.3.The consensus problem of discrete-time second-order multi-agent systems under directed topology is studied.By Lyapunov second method and Schur-Cohn test,a sufficient condition and a necessary and sufficient condition can be obtained to ensure that multi-agent systems can achieve consensus.