Displaying similar documents to “On a dynamics in rational polygonal billiards”

Rational semimodules over the max-plus semiring and geometric approach to discrete event systems

Stéphane Gaubert, Ricardo Katz (2004)

Kybernetika

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We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule 𝒮 n over a semiring 𝒮 is rational if it has a generating family that is a rational subset of 𝒮 n , 𝒮 n being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, rational...