Minimal state space realization of MIMO systems in the max algebra
Bart De Schutter, Bart De Moor · 1995
The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multivariate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to find all equivalent minimal state space realizations of a multiple input multiple output (MIMO) max-linear discrete event system starting from its impulse response matrices. We also give a geometrical description of the set of all minimal state space realizations. 1 Introduction 1.1 Overview In this paper we consider discrete event systems, examples of which are flexible manufacturing systems, subway traffic networks, parallel processing systems, telecommunication networks, . . . . There exists a wide range of frameworks to model and analyze discrete event systems: Petri nets, generalized semi-Markov processes, formal languages, perturbation analysis, comput...