Coherence of Noisy Double-Integrator Networks Without Velocity Measurements

This brief studies the systemic performance of double-integrator consensus networks in the presence of stochastic noises. The systemic performance is characterized in terms of the network coherence, which is equal to the squared H
₁₂
norm of the network and can capture the deviation from network average. Four different types of structured noises are mainly considered and for each type of noise, a consensus protocol without velocity measurements is proposed to guarantee consensus achieving. For the cases with dynamics noise, sensor noise and communication channel noise, it is shown that the network coherence can be explicitly expressed by a function of the nonzero eigenvalues of the Laplacian matrix and the network size. For the case with receiver noise, a sufficient condition is derived to ensure that the network coherence is less than a given constant.