  The noncommutative baby Skyrme model is a Moyal deformation of the
two-dimensional sigma model plus a Skyrme term, with a group-valued or
Grassmannian target. Exact abelian solitonic solutions have been identified
analytically in this model, with a singular commutative limit. Inside any given
Grassmannian, we establish a BPS bound for the energy functional, which is
saturated by these baby Skyrmions. This asserts their stability for unit
charge, as we also test in second-order perturbation theory.
