Explicit solutions of regular linear discrete-time descriptor systems with constant coefficients

Abstract

Explicit solution formulas are presented for systems of the form Ex^k+1 = Ax^k + f^k
with k ∈ K, w here K ⊂ Z is a discrete interval and the pencil λE − A is regular. Different results
are obtained when one starts with an initial condition at the point k = 0 and calculates into the future (i.e., Ex^k+1 = Ax^k + f^k with k ∈ N) and when one wants to get a complete solution (i.e., Ex^k+1 = Ax^k + f^k with k ∈ Z).