A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra |
| |
Authors: | Bart de Schutter Bart de Moor |
| |
Affiliation: | (1) ESAT/SISTA, Katholieke Universiteit Leuven, Kardinaal Mercierlaan 94, B-3001 Leuven, Belgium |
| |
Abstract: | 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 demonstrate that this enables us to solve many important problems in the max algebra and the max-min-plus algebra such as matrix decompositions, construction of matrices with a given characteristic polynomial, state space transformations and the (minimal) state space realization problem.Research assistant with the N.F.W.O. (Belgian National Fund for Scientific Research).Senior research associate with the N.F.W.O. |
| |
Keywords: | max algebra multivariate max-algebraic polynomial equalities and inequalities state space models extended linear complementarity problem |
本文献已被 SpringerLink 等数据库收录! |