Nonnegativity, stability, and regularization of discrete-time descriptor systems

In this paper, for a given descriptor system, we construct a feedback in order to obtain a nonnegative, stable and regular closed-loop system. The required conditions impose structure on the state matrices of the descriptor system, and thereby allow expression of the solution of the new system in terms of smaller matrices. For that, we exploit the structure of the state matrices of the descriptor system. We also design an algorithm to construct the aforementioned feedback and the solution of the closed-loop system. In addition, some examples illustrating the results are presented.