Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation

By introducing delayed state compensation into the normal asynchronously-coupled consensus algorithm, a new consensus algorithm is constructed to solve the dynamical consensus problem of second-order multi-agent systems subjected to communication delay. Based on frequency-domain analysis, a sufficient and necessary condition, which depends on the communication delay and the control parameters, is obtained for two coupled second-order dynamic agents converging to the dynamical consensus, and it is proved that the proposed algorithm can tolerate higher communication delay than the synchronously-coupled consensus algorithm. According to linear fractional transformation and the small-gain theorem, sufficient conditions are gained for second-order multi-agent systems with communication delay under a general digraph. Simulation illustrates the correctness of the results.