  This paper studies a network of observers for a distributed estimation
problem, where each observer assesses a portion of output of a given LTI
system. The goal of each observer is to compute a state estimate that
asymptotically converges to the state of the LTI system. We consider there is a
sparsity constraint that restricts interconnections between observers.
  We provide a sufficient condition for the existence of parameters for the
observers which achieve the convergence of the state estimates to the state of
the LTI system. In particular, this condition can be written in terms of the
eigenvalues of the Laplacian matrix of the underlying communication graph and
the spectral radius of the dynamic matrix of the LTI system.
