Minimal realization in the max algebra is an extended linear complementarity problem
نویسندگان
چکیده
We demonstrate that the minimal state space realization problem in the max algebra can be transformed into an Extended Linear Complementarity Problem (ELCP). We use an algorithm that finds all solutions of an ELCP to find all equivalent minimal state space realizations of a single input single output (SISO) discrete event system. We also give a geometrical description of the set of all minimal realizations of a SISO max-linear discrete event system.
منابع مشابه
Minimal state space realization of MIMO systems in the max algebra
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...
متن کاملMINIMAL STATE SPACE REALIZATION OF MIMO SYSTEMS INTHE MAX ALGEBRA Bart
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 multi-variate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to nd all equivalent minimal state space realizations of a multiple ...
متن کاملA method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra
In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonst...
متن کاملTechnical report bds : 01 - 15 Max - plus - algebraic problems and the extended linear complementarity problem – Algorithmic aspects ∗
Many fundamental problems in the max-plus-algebraic system theory for discrete event systems — among which the minimal state space realization problem — can be solved using an Extended Linear Complementarity Problem (ELCP). We present some new, more efficient methods to solve the ELCP. We show that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (L...
متن کاملThe singular value decomposition in the extended max algebra is an extended linear complementarity problem ∗
We show that the problem of finding a singular value decomposition of a matrix in the extended max algebra can be reformulated as an Extended Linear Complementarity Problem. This allows us to compute all the max-algebraic singular value decompositions of a matrix. This technique can also be used to calculate many other max-algebraic matrix decompositions.
متن کامل