On LMI approach to admissibilization of discrete-time descriptor systems

This paper develops a one-step LMI-based test for the admissibilization of linear discrete-time descriptor systems. For any admissibilizable system, the proposed method can generate a set of constant feedback gain matrices to make the closed-loop system admissible. The technical ingredients of our approach are the projection lemma and the coordinate transformation. The former introduces two instrumental variables into an LMI condition to characterize admissibility and the latter simplifies the representation of compensated descriptor pair by vanishing certain matrix blocks in the equivalent system representation. Combining them with the induced fact that all solution variables to the mentioned LMI condition possess some special block structures, the difficulty of generating nonlinear terms from applying compensation is successfully overcome. The numerical tractability of the results is illustrated by an example.