A stabilization problem for a switched differential-algebraic system is investigated. We propose an approach for solving effectively the stabilization problem for an autonomous linear switched differential-algebraic system based on projector and flow matrices. In switched DAEs, the switches can induce jumps in certain state-variables, and it has been shown that the formulation as a switched DAE already implicitly defines these jumps, no additional jump map must be given. These jumps can be calculated in terms of the consistency projectors. The essence of this method is to design a stabilizing controller for switched differential-algebraic systems, i.e., the continuous dynamics of each subsystem are described by sets of differential-algebraic equations, using an averaging switched DAE model based on consistency projector and flow matrices to guarantee convergence towards an equilibrium point via fast switching