We review some known bounds for eigenvalues of matrices and use similar
techniques to derive bounds for nonlinear eigen problems and the
eigenvalues for LTI systems with delays as a special case. There are two
classes of results. The first are based on Hermitian decompositions, the
second on Gershgorin's theorem. The bounds are easily computable. We
reflect on implications for stability theory, which may be contrasted
with bounds that have been obtained via Riccati stability based on
Lyapunov-Krasovskii theory.