Stability criterion for a linear differential-difference system

A linear differential-difference system of the form
\dot{x}(t)= A_{1}x(t - \tau), x(t)\in R^{n}
is considered, and necessary and sufficient conditions for exponential stability with a given decay rate are derived. The conditions are given in terms of eigenvalues of the matrix A
1
and extend the well-known result for the scalar case.