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

Brüll, Tobias

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

Explicit solution formulas are presented for systems of the form E x^{k+1} = A x^{k} + f^{k} with regular pencil \lambda E − A. Different results are obtained when one starts at k = 0 and calculates into the future (i.e., E x^{k+1} = A x^{k} + f^{k} with k \in \mathbb N) and when one wants to get a complete solution (i.e., E x^{k+1} = A x^{k} + f^{k} with k \in \mathbb Z).