Interval systems over idempotent semiring

Laurent Hardouin (1) , Bertrand Cottenceau (1) , Mehdi Lhommeau (1) , Euriell Le Corronc (1)

1 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés

This paper deals with solution of inequality A ⊗ x ⪯ b , where A, x and b are interval matrices with entries defined over idempotent semiring. It deals also with the computation of a pair of intervals, ( x , y ) which satisfies the equation A ⊗ x = B ⊗ y . It will be shown that this equation may be solved by considering the interval version of the iterative scheme proposed in [R.A. Cuninghame-Green, P. Butkovič, The equation ax = by over ( max , + ) , Theoret. Comput. Sci. 293 (2003) 3–12].

Mots clés: Idempotent semiring; interval analysis; max algebra; Residuation theory

Domaines: Systèmes et contrôle [cs.SY]

Laurent Hardouin, Bertrand Cottenceau, Mehdi Lhommeau, Euriell Le Corronc. Interval systems over idempotent semiring. Linear Algebra and its Applications, 2009, 431 (5–7), pp.855 - 862. ⟨10.1016/j.laa.2009.03.039⟩. ⟨hal-01113461⟩