### Abstract

Consider an affine system with a polytope as state set. State trajectories are terminated when they reach a facet of the polytope and attempt to exit. The realization problem is considered based on the behavior of the system, i.e. the set of input-output trajectories on time-intervals of either finite or infinite length. The state set can be affinely reduced due to non-observability if and only if a subspace of the classical unobservable subspace, characterized using the normal vectors of the exit facets, is
nontrivial.

Original language | English |
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Title of host publication | Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002) |

Editors | D.S. Gilliam, J. Rosenthal |

Publication status | Published - 2002 |

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## Cite this

Habets, L. C. G. J. M., & Schuppen, van, J. H. (2002). Reduction of affine systems on polytopes. In D. S. Gilliam, & J. Rosenthal (Eds.),

*Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002)*