On the robustness of linear continuous-time dynamic systems

In this note, for a given linear continuous-time dynamic system
\dot{x} = Ax + Bu
, we determine sufficient conditions for the existence of a constant feedback matrix
k
such that the closed-loop system matrix
A - Bk
admits a diagonal positive solution of the Lyapunov equation. An algorithm for the determination of such
k
matrix is given and some examples are solved.