Journal Article

On the anticipation phenomenon for implicit linear discrete-time systems on finite intervals

M. KOCIÉCKI and K. M. PRZYLUSKI

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 13, issue 3, pages 211-221
Published in print September 1996 | ISSN: 0265-0754
e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/13.3.211
On the anticipation phenomenon for implicit linear discrete-time systems on finite intervals

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Implicit linear discrete-time systems are systems described by the difference equation Exk+1 = Fxk + Guk. It is well known that, for such systems, the current value of a trajectory (xk) may be dependent on future values of an input sequence (uk). This property, which is called the anticipation phenomenon, has previously been studied by the authors for k running through the whole set of nonnegative integers. In this paper, we study this phenomenon for systems defined on finite intervals. In particular, we give a quantitative characterization of anticipation phenomenon by introducing the so-called anticipation index of a system.

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Subjects: Mathematics

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