Robust synchronization of dynamical networks with compensation of disturbances

In this paper, a robust output control scheme is proposed for a linear dynamical network such that every its local subsystem is described by a linear differential equation with a priori unknown parameters. The network is subject to unknown exogenous bounded disturbances. The considerations are based on the introduction of a directed graph with vertices associated with the corresponding nodes of the network. An algorithm is proposed which ensures the synchronization of the network along with the compensation of the unknown disturbances with required accuracy. It is shown that the proposed scheme also remains valid for a network associated with an undirected graph. The theoretical results are illustrated via a numerical example of a network with four nodes.