12. Application to Systems Analysis by Mixed Matrices
Kazuo Murota · Society for Industrial and Applied Mathematics eBooks · 2003
This chapter presents an application of discrete convex analysis to systems analysis by mixed matrices. Motivated by a physical observation to distinguish two kinds of numbers appearing in descriptions of physical/engineering systems, the concepts of mixed matrices and mixed polynomial matrices are introduced as mathematical tools for dealing with two kinds of numbers in systems analysis. Discrete convex functions arise naturally in this context and the discrete duality theorems are vital for the analysis of the rank of mixed matrices and the degree of determinants of mixed polynomial matrices.