Consensus conditions for higher-order descriptor multi-agent systems with communication time-delays

In this paper, the consensus problem for higher-order descriptor multi-agent systems (DMASs) with time-delays is investigated. Firstly, a distributed consensus protocol based on output feedback is proposed. Secondly, the state transformation is presented to convert the consensus problem into the stability problem. Based on the Lyapunov theory and the linear matrix inequality (LMI) method, sufficient conditions in terms of LMIs are derived to ensure that consensus of DMASs can be achieved. Moreover, the consensus problem for higher-order DMASs with delays is solved under two cases where interaction topologies are undirected and directed, which is more complicated and challenging. Finally, numerical simulations are provided to demonstrate the effectiveness of our results.