A Lyapunov theory for linear time-delay systems

Some relationships between a Lyapunov based stability test and linear control system models with time delays are explored. The main result is a generalization of the result that if (
A, B
) is a reachable pair of matrices, then square
A
is a stability matrix if and only if there is a positive-definite matrix
K
such that
AK + KA' = - BB'
.