Sufficient and Necessary Conditions for Leader-Following Consensus of Second-Order Multi-Agent Systems via Intermittent Sampled Control

Continuous control protocols are extensively utilized in traditional MASs, in which information needs to be transmitted among agents consecutively, therefore resulting in excessive consumption of limited resources. To decrease the control cost, based on ISC, several LFC problems are investigated for second-order MASs without and with time delay, respectively. Firstly, an intermittent sampled controller is designed, and a sufficient and necessary condition is derived, under which state errors between the leader and all the followers approach zero asymptotically. Considering that time delay is inevitable, a new protocol is proposed to deal with the time-delay situation. The error system’s stability is analyzed using the Schur stability theorem, and sufficient and necessary conditions for LFC are obtained, which are closely associated with the coupling gain, the system parameters, and the network structure. Furthermore, for the case where the current position and velocity information are not available, a distributed protocol is designed that depends only on the sampled position information. The sufficient and necessary conditions for LFC are also given. The results show that second-order MASs can achieve the LFC if and only if the system parameters satisfy the inequalities proposed in the paper. Finally, the correctness of the obtained results is verified by numerical simulations.