  In this paper, we address the problem of solving infinite-dimensional
harmonic algebraic Lyapunov and Riccati equations up to an arbitrary small
error. This question is of major practical importance for analysis and
stabilization of periodic systems including tracking of periodic trajectories.
We first give a closed form of a Floquet factorization in the general setting
of L 2 matrix functions and study the spectral properties of
infinite-dimensional harmonic matrices and their truncated version. This
spectral study allows us to propose a generic and numerically efficient
algorithm to solve infinite-dimensional harmonic algebraic Lyapunov equations
up to an arbitrary small error. We combine this algorithm with the Kleinman
algorithm to solve infinite-dimensional harmonic Riccati equations and we apply
the proposed results to the design of a harmonic LQ control with periodic
trajectory tracking.
