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IMA Journal of Mathematical Control and Information 1995 12(1):17-36; doi:10.1093/imamci/12.1.17
© 1995 by Institute of Mathematics and its Applications
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State models and asymptotic behaviour of 2D positive systems

MARIA ELENA VALCHER and ETTORE FORNASINI

Dipartimento di Elettronica ed Informatica, Univ. di Padova via Gradenigo 6a, 35131 Padova, Italy

Homogeneous 2D positive systems are 2D state-space models whose variables are alwalys nonnegative and, consequently, are described by a pair of nonnegative square matrices (A, B). In the paper, the properties of these pairs are discussed both in the general case and under particular assumptions like finite memory, separability, and property L.

Various aspects of the positive asymptotic dynamic are considered; in particular, sufficient conditions are provided guaranteeing that the local states are eventually strictly positive. Finally, some results on the convergence of the states towards a constant asymptotic distribution are presented.


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