We apply the linear matrix inequality method to consensus and consensus problems of the single integrator multiagent system with heterogeneous delays in directed networks. To overcome the difficulty caused by heterogeneous time-varying delays, we rewrite the multiagent system into a partially reduced-order system and an integral system. As a result, a particular Lyapunov function is constructed to derive sufficient conditions for consensus of multiagent systems with fixed (switched) topologies. We also apply this method to the consensus of multiagent systems with disturbances and heterogeneous delays. Numerical examples are given to illustrate the theoretical results.
" Consensus for Multiagent Systems with Heterogeneous Time-Varying Delays." Abstr. Appl. Anal. 2013 (SI18) 1 - 8, 2013. https://doi.org/10.1155/2013/576290