  We extend the recently developed generalized Floquet theory [Phys. Rev. Lett.
110, 170602 (2013)] to systems with infinite memory. In particular, we show
that a lower asymptotic bound exists for the Floquet exponents associated to
such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian
particle, and a circuit resonator with an ideal transmission line. All these
examples show the usefulness of this new approach to the study of dynamical
systems with memory, which are ubiquitous in science and technology.
