Robust Bounds on the Eigenvalues of Linear Systems with Delays and Their Applications

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.