Distributed Consensus Tracking of Multi-Agent Systems with Time-varying Input/Output Delays and Mismatched Disturbances

This paper investigates the distributed consensus tracking control problem for general linear multi-agent systems (MASs) with bounded time-varying input/output delays and mismatched disturbances under a directed communication graph containing a spanning tree. First, a part of the mismatched disturbances is transformed into the input channel as the matched disturbance, that allows the deployment of a predictive extended state observer (ESO) in order to estimate the consensus tracking error and transformed matched disturbance simultaneously. Subsequently, the ESO is used for designing a controller. The stability of the closed-loop system is guaranteed via a Lyapunov-Krasovskii functional with sufficient conditions in terms of delay-dependent linear matrix inequalities (LMIs). An additional 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 be feasible without it. The efficacy of the proposed scheme is demonstrated via simple numerical examples.