Reachability and observability of linear systems over max-plus
Kybernetika, Tome 35 (1999) no. 1, p. [2].

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This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable case, a duality is shown to exist between the two properties.
Classification : 15A80, 93B03, 93B05, 93B07, 93B25, 93C65, 93C83
Mots-clés : reachability; observability; linear system; max-plus algebra 
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Gazarik, Michael J.; Kamen, Edward W. Reachability and observability of linear systems over max-plus. Kybernetika, Tome 35 (1999) no. 1, p. [2]. https://geodesic-test.mathdoc.fr/item/KYB_1999__35_1_a1/