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

This paper investigates the distributed consensus tracking control problem for general linear multi-agent systems with external disturbances and heterogeneous time-varying input communication delays under a directed graph topology, containing spanning tree. First, all agents whose state matrix has no eigenvalues positive real parts, communication-delay-related observer, which is used to construct controller, designed followers estimate leader’s information. Second, by means of output regulation theory, results are relaxed case that only needs be asymptotically stable or marginally and, these conditions, controller redesigned. Both cases lead closed-loop error system stability guaranteed via Lyapunov–Krasovskii functional sufficient conditions in terms input-delay-dependent inequalities (LMIs). An extended LMI proposed which, conjunction rest LMIs, solution larger upper bound on than what would feasible without it. It highlighted integration observer input-delay-related fully (which requires global information) scalable arbitrarily large networks. The efficacy scheme demonstrated an illustrative numerical example.