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Singular systems of partial difference equations

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Abstract

Sufficient conditions for the existence and uniqueness of solutions of singular systems of 2-D difference equations with constant coefficients are formulated. Linear transformation of the matrix coefficients leads to recursive forms of such systems of equations. The results are applied to standard 2-D state-space models of discrete systems and sufficient conditions of BIBO stability of these singular systems are obtained.

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Abbreviations

R, Z, Z + :

sets of reals, integers, nonnegative integers, resp.

A, B, C, ... :

matrices, subsets ofZ n

A ik :

blocks of matrixA

I r, Nr :

unit matrix, nilpotent matrix of orderr

x, y, u, ... :

vector sequences, i.e., mappingsZ n →R m

\((x)_{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} } ,(Ax)_{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} } \) :

the lastr components of the vectorx orAx, resp

\((x)_{\bar r} ,(Ax)_{\bar r} \) :

the firstr components of the vectorx orAx, resp

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Authors and Affiliations

  1. Department of Mathematics, Czech Technical University, Prague, Czechoslovakia

    JiŘÍ Gregor

Authors
  1. JiŘÍ Gregor
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Gregor, J. Singular systems of partial difference equations. Multidim Syst Sign Process 4, 67–82 (1993). https://doi.org/10.1007/BF00986006

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  • DOI: https://doi.org/10.1007/BF00986006

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