Murota K. Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability

Berlin: Springer, 1987. — 291 p.Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated using graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful mathematical modelings. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach. This book is of interest to graduate students and researchers.Preliminaries.
Graph-Theoretic Approach to the Solvability of a System of Equations.
Graph-Theoretic Approach to the Controllability of a Dynamical System.
Physical Observations for Faithful Formulations.
Matroid-Theoretic Approach to the Solvability of a System of Equations.
Matroid-Theoretic Approach to the Controllability of a Dynamical System.