Nonnegative singular control systems using the Drazin projector

In this work we study conditions for guaranteeing the nonnegativity of a discrete-time singular control system. A first approach can be found in the literature for general systems, using the whole coefficient matrices. Also, the particular case of matrices of index 1 has been treated by using a block decomposition and the group-projector of the matrix that gives the singularity to the system. In order to complete this study, an analysis of the nonnegativity of a singular control system for matrices having arbitrary index is done by means of the core-nilpotent decomposition. This technique allows us to reduce the size of the original matrices, improving the results where the whole coefficients are involved.