  Looped-functionals have been shown to be relevant for the analysis of a wide
variety of systems. However, the conditions obtained in previous works on the
analysis of sampled-data, impulsive and switched systems have only been shown
to be sufficient for the characterization of their associated discrete-time
stability conditions. We prove here that these conditions are also \necessary.
This result is derived for a wider class of linear systems, referred to as
impulsive pseudo-periodic systems, that encompass periodic, impulsive,
sampled-data and switched systems as special cases.
