Synchronization of multi-agent systems with directed topologies and heterogeneous delays

Abstract

An algorithm for synchronization of a linear multi-agent system with directed topology is derived. Time delays in the control loop are taken into account when designing the control, these delays need not be equal for all agents. The Lyapunov-Krasovskii functional is used, the algorithm is formulated by means of linear matrix inequalities. It is shown that different values of the time delay can lead to an error in synchronization that does not converge to zero. A bound on this error is derived. Examples are presented to illustrate the proposed algorithm.