In this paper equivalent conditions for exact observability of diagonal sys
tems with a finite-dimensional output operator are given. One of these equi
valent conditions is the conjecture of Russell and Weiss (SIAM J. Control O
pt. 32(1) (1994) 1-23). The other conditions are in terms of the eigenvalue
s and the Lyapunov solutions of finite-dimensional subsystems. (C) 2001 Els
evier Science B.V. All rights reserved.