State models and asymptotic behaviour of 2D positive systems
- 1 March 1995
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Mathematical Control and Information
- Vol. 12 (1) , 17-36
- https://doi.org/10.1093/imamci/12.1.17
Abstract
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.Keywords
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