  This paper is concerned with the problem of distributed estimation for
time-varying interconnected dynamic systems with arbitrary coupling structures.
To guarantee the robustness of the designed estimators, novel distributed
stability conditions are proposed with only local information and the
information from neighbors. Then, simplified stability conditions which do not
require timely exchange of neighbors' estimator gain information is further
developed for systems with delayed communication. By merging these
subsystem-level stability conditions and the optimization-based estimator gain
design, the distributed, stable and optimal estimators are proposed. Quite
notably, these optimization solutions can be easily obtained by standard
software packages, and it is also shown that the designed estimators are
scalable in the sense of adding or subtracting subsystems. Finally, an
illustrative example is employed to show the effectiveness of the proposed
methods.
