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IMA Journal of Mathematical Control and Information 1996 13(3):211-221; doi:10.1093/imamci/13.3.211
© 1996 by Institute of Mathematics and its Applications
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On the anticipation phenomenon for implicit linear discrete-time systems on finite intervals

M. KOCIÉCKI and K. M. PRZYLUSKI

Polish Telecom Swietokrzyska 3, 00-945 Warszawa, Poland
Institute of Mathematics, Polish Academy of Sciences Sniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland

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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