Adaptive synchronization of linear multi-agent systems with time-varying multiple delays

In this paper we consider the synchronization problem of continuous high-order linear agents sharing information through a communication network. The presence of communication delays implies that the distributed control protocol has to be implemented via outdated information. Delays are here considered as time-varying functions associated to each specific communication link. The cooperative tracking of the leader is achieved through a fully distributed control algorithm leveraging on a local adaptive strategy that weights the delayed information for all communication topologies in which the leading agent is globally reachable. In the analytical derivation the different time-varying delays are variables to be tackled simultaneously in the solution of the synchronization problem and the delay-dependent stability criterion is provided by combining the Lyapunov-Krasovskii functional with the Linear Matrix Inequality (LMI) approach. The LMI criterion provides the estimate of the delay upper bound that ensures the stability margin and it can be easily verified by using standard algorithms, such as the interior-point one. Some representative examples illustrate the theoretical results and show the effectiveness of the proposed approach.