Considering the use of the so-called Composite Quadratic Lyapunov Function (CQLF) based on descriptor techniques from the stability theory of continuous systems, this paper designs a linear feedback control to deal with bounded uncertainties in a class of nonlinear dynamical system described by semi-explicit Differential Algebraic Equations (DAE) by application of an extended version of the conventional Attractive Invariant Ellipsoid Method (AEM). The resulting closed-loop system converges to a minimal size set generated by the convex hull of some ellipsoids. The use of CQLF in the modified AEM allows obtaining an appropriate feedback control to ensure robustness and stability properties of the system. An academic example is presented to illustrate the applicability of the contribution.