Nonnegative singular control systems using the Drazin projector

In this paper we study conditions to guarantee the nonnegativity of a discretetime singular control system. A first approach can be found in the literature for general systems by using the entire 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 entire coefficients are involved.