Natural consensus filters for second order infinite dimensional systems

This work proposes consensus filters for a class of second order infinite dimensional systems. The proposed structure of the consensus filters is that of a local filter written in the natural setting of a second order formulation with the additional coupling that enforces consensus by minimizing the disagreement between all local filters. An advantage of the second order formulation imposed on the local filters is the natural interpretation that they retain, namely that the time derivative of the estimated position is equal to the estimated velocity. Stability analysis of the collective dynamics is achieved via the use of a parameter-dependent Lyapunov functional, and which guarantees that asymptotically, all filters agree with each other and that they all converge to the true state of the second order system.