  We analyse stability of observability estimates for solutions to wave and
Scr\" odinger equations subjected to additive perturbations. The paper
generalises the recent averaged observability/control result by allowing for
systems consisting of operators of different types. The method also applies to
the simultaneous observability problem by which one tries to estimate the
energy of each component of a system under consideration. The analysis relies
on microlocal defect tools; in particular on standard H-measures, when the main
dynamic of the system is governed by the wave operator, while parabolic
H-measures are explored in the case of the Schr\" odinger operator.
