A Method to Find All Solutions of a System of Multivariate Polynomial Equalities and Inequalities in the Max Algebra

Reference

B. De Schutter and B. De Moor, "A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra," Discrete Event Dynamic Systems: Theory and Applications, vol. 6, no. 2, pp. 115-138, Mar. 1996.

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.

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BibTeX

@article{DeSDeM:93-71,
   author  = {De Schutter, Bart and De Moor, Bart},
   title   = {A Method to Find All Solutions of a System of Multivariate
              Polynomial Equalities and Inequalities in the Max Algebra},
   journal = {Discrete Event Dynamic Systems: Theory and Applications},
   volume  = {6},
   number  = {2},
   pages   = {115--138},
   month   = mar,
   year    = {1996}
   }


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