  We develop an eigenvalue-based approach for the stability assessment and
stabilization of linear systems with multiple delays and periodic coefficient
matrices. Delays and period are assumed commensurate numbers, such that the
Floquet multipliers can be characterized as eigenvalues of the monodromy
operator and by the solutions of a finite-dimensional non-linear eigenvalue
problem, where the evaluation of the characteristic matrix involves solving an
initial value problem. We demonstrate that such a dual interpretation can be
exploited in a two-stage approach for computing dominant Floquet multipliers,
where global approximation is combined with local corrections. Correspondingly,
we also propose two novel characterizations of left eigenvectors. Finally, from
the nonlinear eigenvalue problem formulation, we derive computationally
tractable expressions for derivatives of Floquet multipliers with respect to
parameters, which are beneficial in the context of stability optimization.
Several numerical examples show the efficacy and applicability of the presented
results.
