Linear Discrete-Time Descriptor Systems

We consider linear discrete-time descriptor systems, i.e. systems of linear equations of the form $E_{k+1} x_{k+1} = A_k x_k + f_k$, where $E_k$ and $A_k$ are matrices, $f_k$ are vectors and $x_k$ are the vectors of the solution we are looking for. Analogously to the book "Differential-Algebraic Equations - Analysis and Numerical Solution" by V.Mehrmann and P.Kunkel the existence and uniqueness of solutions is first studied for the constant coefficient case, i.e. where $E_k = E$ and $A_k = A$ and then for the variable coefficient case. A strangeness index is defined for such systems