  Motivated by recent experimental results on GdRu$_2$Si$_2$ [Khanh, N.D.,
Nakajima, T., Yu, X. et al., \emph{Nat. Nanotechnol.} \textbf{15}, 444-449
(2020)], where nanometric square skyrmion lattice was observed, we propose
simple analytical mean-field description of the high-temperature part of the
phase diagram of centrosymmetric tetragonal frustrated antiferromagnets with
dipolar interaction in the external magnetic field. In the reciprocal space
dipolar forces provide momentum dependent biaxial anisotropy. It is shown that
in tetragonal lattice in the large part of the Brillouin zone for mutually
perpendicular modulation vectors in the $ab$ plane this anisotropy has mutually
perpendicular easy axes and collinear middle axes, what leads to double-Q
modulated spin structure stabilization. The latter turns out to be a square
skyrmion lattice in the large part of its stability region with the topological
charge $\pm 1$ per magnetic unit cell, which is determined by the frustrated
exchange coupling, and, thus, nanometer-sized. In the presence of additional
single-ion easy-axis anisotropy, easy and middle axes can be swapped, which
leads to different phase diagram. It is argued that the latter case is relevant
to GdRu$_2$Si$_2$.
