Reference
Y. Zeinaly,
J. H. van Schuppen, and B. De
Schutter, "Linear positive systems may have a reachable subset from the origin
that is either polyhedral or nonpolyhedral,"
SIAM Journal on
Matrix Analysis and Applications, vol. 41, no. 1, pp. 297-307, 2020.
Abstract
Positive systems with positive inputs and positive outputs are used in several
branches of engineering, biochemistry, and economics. Both control theory and
system theory require the concept of reachability of a time-invariant
discrete-time linear positive system. The subset of the state set that is
reachable from the origin is therefore of interest. The reachable subset is in
general a cone in the positive vector space of the positive real numbers. It is
established in this paper that the reachable subset can be either a polyhedral
or a nonpolyhedral cone. For a single-input case, a characterization is
provided of when the infinite-time and the finite-time reachable subset are
polyhedral. An example is provided for which the reachable subset is
nonpolyhedral. Finally, for the case of polyhedral reachable subset(s), a
method is provided to verify if a target set can be reached from the origin
using positive inputs.
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BibTeX
@article{ZeiDeS:20-017,
author = {Zeinaly, Yashar and van Schuppen, Jan H. and De Schutter, Bart},
title = {Linear Positive Systems May Have a Reachable Subset from the
Origin That is Either Polyhedral or Nonpolyhedral},
journal = {SIAM Journal on Matrix Analysis and Applications},
volume = {41},
number = {1},
pages = {297--307},
year = {2020}
}