This paper addresses the problem of robustly stabilising a class of linear differential-algebraic systems characterised by autonomous and asymptotically stable zero dynamics, in spite of parameter uncertainties ranging over a priori fixed bounded sets. We exploit recent results related to the structural properties and normal forms of this class of systems and propose a robust control that asymptotically recovers, in practical terms, the performance of a nominal, though non-implementable, stabilising control. The proposed control combines a partial output feedback control, aimed at letting the system behave as a regular system, and a robust control, based on an extended observer, using which the dynamic of the closed loop system is rendered arbitrarily close to the one of a properly selected stable system. The extended observer, originally conceived in the context of standard differential systems, is here shown to be the key ingredient for robustly stabilising the targeted class of differential-algebraic systems.