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Explicit solutions of regular linear discrete-time descriptor systems with constant coefficients. (English) Zbl 1189.39001

Summary: Explicit solution formulas are presented for systems of the form \(Ex^{k+1}=Ax^k+f^k\) with \(k \in \mathbb K\), where \(\mathbb K\subset \mathbb Z\) is a discrete interval and the pencil \(\lambda E-A\) 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 \(k\in\mathbb N\)) and when one wants to get a complete solution (i.e., \(Ex^{k+1}=Ax^k+f^k\) with \(k\in \mathbb Z\)).

MSC:

39A06 Linear difference equations
93C55 Discrete-time control/observation systems
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