Interval max-plus systems of linear equations

Finite-Horizon Min-Max Control of Max-Plus-Linear Systems

In this note, we provide a solution to a class of finite-horizon min–max control problems for uncertain max-plus-linear systems where the uncertain parameters are assumed to lie in a given convex and compact set, and it is required that the closed-loop input and state sequence satisfy a given set of linear inequality constraints for all admissible uncertainty realizations. We provide sufficient...

A stabilizing model predictive controller for uncertain max-plus-linear systems and uncertain switching max-plus-linear systems ⋆

We first discuss conditions for stability for uncertain max-plus-linear systems and for uncertain switching max-plus-linear systems, where in the uncertainty description the system matrices live in a union of polyhedra. Based on the newly derived stability conditions, a stabilizing model predictive controller is derived for both uncertain max-plus-linear systems and uncertain switching max-plus...

Solvability of Systems of Linear Interval Equations

Max-plus algebra and max-plus linear discrete event systems: An introduction

We provide an introduction to the max-plus algebra and explain how it can be used to model a specific class of discrete event systems with synchronization but no concurrency. Such systems are called max-plus linear discrete event systems because they can be described by a model that is “linear” in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how thes...

Duality in linear interval equations

In this paper we nd solution of linear interval equation in dual form based on the generalizedprocedure of interval extension which is called interval extended zero method.Moreover, proposed method has signicant advantage, is that it substantially decreasesthe excess width eect.