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This paper investigates the distributed consensus tracking control problemfor general linear multi-agent systems (MASs) with external disturbances andheterogeneous time-varying input and communication delays under a directedcommunication graph topology, containing a spanning tree. First, for all agentswhose state matrix has no eigenvalues with positive real parts, acommunication-delay-related observer, which is used to construct thecontroller, is designed for followers to estimate the leader's stateinformation. Second, by means of the output regulation theory, the results arerelaxed to the case that only the leader's state matrix eigenvalues havenon-positive real parts and, under these relaxed conditions, the controller isredesigned. Both cases lead to a closed-loop error system of which thestability is guaranteed via a Lyapunov-Krasovskii functional with sufficientconditions in terms of input-delay-dependent linear matrix inequalities (LMIs).An extended LMI is proposed which, in conjunction with the rest of LMIs,results in a solution with a larger upper bound on delays than what would befeasible without it. It is highlighted that the integration ofcommunication-delay-related observer and input-delay-related LMI to construct afully distributed controller (which requires no global information) is scalableto arbitrarily large networks. The efficacy of the proposed scheme isdemonstrated via illustrative numerical examples.

Multi-agent consensus with heterogeneous time-varying input and communication delays in digraphs