Duality and interval analysis over idempotent semirings

Abstract

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A\otimes X⪯B$. The purpose of this paper is to consider a dual product, denoted $\odot$, and the dual residuation of matrices, in order to solve the following inequality $A\otimes X⪯X⪯B\odot X$. Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals.

References in corpus (3)

• Duality and separation theorems in idempotent semimodules
• Observer Design for (max,plus) Linear System
• Interval systems over idempotent semiring

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• Analysis of P-time Event Graphs in (Max,+) and (Min,+) Algebras