  We introduce the class of perturbed right-angled Artin groups. These are
constructed by gluing Bieri double groups into standard right-angled Artin
groups. As a first application of this construction we obtain families of
CAT(0) groups containing finitely presented subgroups which are not of type
$\mathrm{FP}_3$, and have exponential, or polynomial Dehn functions of
prescribed degree.
