  This paper studies the optimal state estimation problem for interconnected
systems. Each subsystem can obtain its own measurement in real time, while, the
measurements transmitted between the subsystems suffer from random delay. The
optimal estimator is analytically designed for minimizing the conditional error
covariance. The boundedness of the expected error covariance (EEC) is analyzed.
In particular, a new condition that is easy to verify is established for the
boundedness of EEC. Further, the properties of EEC with respect to the delay
probability are studied. We found that there exists a critical probability such
that the EEC is bounded if the delay probability is below the critical
probability. Also, a lower and upper bound of the critical probability is
derived. Finally, the proposed results are applied to a power system, and the
effectiveness of the designed methods is illustrated by simulations.
