A state and unknown input estimation is carried out for a class of non linear systems with unknown inputs whose dynamics is governed by differential-algebraic equations (DAE). We propose to replace the original DAE for a system with only differential equations by using a zeroing manifold algorithm inducing a state space dimension reduction. Nevertheless, the observability conditions may be checked in terms of the original system. Finally, the state estimation is carried out by using a sliding mode high order differentiator.