Linear positive systems may have a reachable subset from the origin that is either polyhedral or nonpolyhedral

Linear positive systems may have a reachable subset from the origin that is either polyhedral or nonpolyhedral

Zeinaly, Y. (TU Delft Team Bart De Schutter)
van Schuppen, J.H. (TU Delft Mathematical Physics)
De Schutter, B.H.K. (TU Delft Delft Center for Systems and Control; TU Delft Team Bart De Schutter)

Delft Center for Systems and Control

2020

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 subsets 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.

Linear positive systems
Polyhedral cone
Positive recursion
Reachable subset

http://resolver.tudelft.nl/uuid:04d0c57d-3a70-41c2-980a-674fd0bd06af

https://doi.org/10.1137/19M1268161

0895-4798

SIAM Journal on Matrix Analysis and Applications, 41 (1), 279-307

Institutional Repository

journal article

© 2020 Y. Zeinaly, J.H. van Schuppen, B.H.K. De Schutter