**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.

Online version of the paper

Corresponding technical report: pdf file (1.63 MB)

@article{ZeiDeS:20-017,

author={Y. Zeinaly and J.H. van Schuppen and B. {D}e Schutter},

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},

doi={10.1137/19M1268161}

}

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