Control dynamical systems have many applications in different areas
of science and technology, for example, in circuit theory,
economics, chemistry, population studies, etc. That is why this
thesis focuses on the study of singular control systems in discrete
time, with particular attention to their nonnegativity property. 

The study of the general problem is divided in two situations. The first
one deals with the initial case corresponding to matrices of index
1. This case has special characteristics with respect to the general
one. The study of the nonnegativity of singular control systems of 
index greater than 1 is  implemented from the index 1 case. 
In both cases the matrix results previously obtained has been used.

Then, firstly several sets of matrices involving the nonnegativity
of a matrix, of its group inverse, of its group projector or
different combinations between them are introduced. Characterizations 
of these sets have been obtained. As a special case, group 
{l}-periodic matrices are also studied.

Next, the nonnegativity of singular control systems of the form 
(E,A,B,C) is analyzed. Initially, a result that uses the coefficient
matrices to establish a characterization of the nonnegativity of a
control system is presented. Later, the matrix results obtained
above allow to derive another characterization involving only blocks
of the aforementioned coefficient matrices (suitably modified)
instead of the complete matrices. This fact will contribute to
saving operations when analyzing the nonnegativity of a control
system.

Then, the corresponding sets for matrices with index greater than 1 are
defined. In this case, the main algebraic tool used is the core-nilpotent
decomposition of a square matrix. So, characterizations of these
sets are obtained. Again, the Drazin {l}-periodic matrices are introduced 
and characterized.

Finally, the obtained results are applied to study the
characterization of the nonnegativity of a singular control system
whose matrix E has index greater than 1.