Observability properties of the periodic Toda lattice

We consider observability properties of the periodic Toda lattice and show that the system is observable by measuring the momentum of one mass and the exponential of the distance of the same mass to a neighboring mass. Furthermore, we discuss coordinate transformations of the system and apply different local observer design methods to locally observe a specific solution of the periodic Toda lattice. All discussed local observer design methods show poor convergence properties. An observability gramian analysis reveals the difficulty of the observer design problem for the periodic Toda lattice.