In this paper descriptor feedback control of high index or even non-regular linear discrete-time descriptor systems is considered. The approach is based on a linear matrix inequality (LMI) characterization (with a Lyapunov-type matrix as matrix variable) of stable and causal descriptor systems. Applying this result to the problem of stabilizing a controlled discrete-time descriptor system by descriptor feedback such that the closed loop is causal, renders a nonlinear matrix inequality with the controller gain matrix and a Lyapunov-type matrix as variables. For the corresponding non-descriptor problem this matrix inequality can be reduced to an LMI by applying Schur’s Lemma and a subsequent linearizing change of variables. In the descriptor setup this procedure is not applicable due to the indefiniteness of the occurring Lyapunov-type matrix. Instead, here a two step controller computation is presented, which firstly renders the closed loop system causal. In the second step an LMI based procedure is used to guarantee stability without affecting causality of the closed loop.