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EXPLICITSOLUTIONSOFREGULARLINEARDISCRETE-TIMEDESCRIPTORSYSTEMSWITHCONSTANTCOEFFICIENTS ELA

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ELA

EXPLICIT SOLUTIONS OF REGULAR LINEAR DISCRETE-TIME DESCRIPTOR SYSTEMS WITH CONSTANT COEFFICIENTS

∗

TOBIAS BR ¨ULL†

Abstract. Explicit solution formulas are presented for systems of the formExk+1=Axk+fk withk∈K, w hereK⊂Zis a discrete interval and the pencil λE−Ais regular. Different results are obtained when one starts with an initial condition at the point k= 0 and calculates into the future (i.e.,Exk+1 =Axk+fk withk∈N) and when one wants to get a complete solution (i.e., Exk+1=Axk+fkwithk∈Z).

Key words. Descriptor system, Strangeness index, Linear discrete descriptor system, Explicit solution, Backward Leslie model.

AMS subject classifications.39A05, 15A06.

∗ Received by the editors January 23, 2009. Accepted for publication July 3, 2009. Handling Editor: Peter Lancaster. This research is supported by the DFG Research Center MATHEONin Berlin.

†Institut f¨ur Mathematik, TU Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany ([email protected]).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 317-338, July 2009

http://math.technion.ac.il/iic/ela

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