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This work presents a new method to design consensus controllers for perturbeddouble integrator systems whose interconnection is described by a directedgraph containing a rooted spanning tree. We propose new robust controllers tosolve the consensus and synchronization problems when the systems are under theeffects of matched and unmatched disturbances. In both problems, we presentsimple continuous controllers, whose integral actions allow us to handle thedisturbances. A rigorous stability analysis based on Lyapunov's direct methodfor unperturbed networked systems is presented. To assess the performance ofour result, a representative simulation study is presented.

Robust Integral Consensus Control of Multi-Agent Networks Perturbed by Matched and Unmatched Disturbances: The Case of Directed Graphs