Dynamic systems described by an implicit mixed set of Differential and Algebraic Equations (DAEs) are often encountered in control system modeling and analysis due to inherent constraints in the system. A key difficulty in control and simulation of DAE systems is that they are not expressed in an explicit state space representation. This paper describes a general approach based on singular perturbation analysis for adding fast dynamics to a system of DAEs so that they can be expressed in an explicit state space form. Conditions for asymptotic convergence and approximation methods are investigated. The approach is illustrated for a model of a two-phase flow heat exchanger.