State/Driving-Variable Representation of 2D Systems

Authors:
Isabel Brás;Paula Rocha
Affiliations:
Department of Mathematics, University of Aveiro, Portugal isabelb@mat.ua.pt;Department of Mathematics, University of Aveiro, Portugal procha@mat.ua.pt
Venue:
Multidimensional Systems and Signal Processing
Year:
2002

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Abstract

We characterize the discrete 2D systems with kernel representation that admit a state/driving-variable (SDV) representation. This characterization is based on the possibility of decomposing a behaviour {\cal B} as the sum of its controllable part with a suitable autonomous part (controllable-autonomous decomposition). We show that {\cal B} has a SDV representation if and only if it allows for a controllable-autonomous decomposition where the autonomous part is SDV representable. This means that {\cal B} has a kernel representation matrix which can be decomposed as the product of two 2D L-polynomial matrices such that the left factor is factor left prime and the right factor is square and properly invertible.