Fault-tolerant consensus in oscillator networks with assignment of agreement laws and dynamics

In this paper we face a consensus problem stated for networks where the agents are identical oscillators. The first special feature of our problem is that the agents share a partial information on their states through communication apparatuses which are subject to faults. Moreover, we require that the agreement laws and the dominant dynamics towards the consensus manifold are arbitrarily prespecified and not affected by the faults. Our results are constituted by a necessary and sufficient solvability condition, together with explicit formulas for high-gain regulators.