Systems Analysis by Graphs and Matroids: Structural Solvability and ControllabilityRecent 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 by means of 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. |
Contents
Introduction | 1 |
Chapter 2 | 28 |
Decompositions of a Graph by Mengertype Linkings | 41 |
Copyright | |
13 other sections not shown
Other editions - View all
Systems Analysis by Graphs and Matroids: Structural Solvability and ... Kazuo Murota Limited preview - 2012 |
Common terms and phrases
A-sF algebraically independent algorithm arc-set arcs associated bipartite graph assumption auxiliary graph auxiliary network B₁ base blocks C₁ coefficient matrix column-set columns combinatorial canonical form components computation consider corresponding decomposition defined deg p(s denoted descriptor form descriptor system 12.3 dimensional analysis dimensions DM-decomposition dynamical degree dynamical system electrical network equivalent Example exists expressed feedback vertex set flow f given graph G graph-theoretic greatest common divisor independent over Q independent-flow problem Jacobian matrix Japanese layered mixed matrix M-components mathematical matrix D(s matroid-theoretic maximum independent flow maximum matching Murota nonsingular nonvanishing entries obtained partial order permutation permutation matrix physical polymatroid polynomial Proof Prop Proposition rational numbers representation graph respectively row-set signal-flow graph standard form 12.1 structural controllability structural solvability submatrix subproblems subset system of equations term-rank Theorem totally unimodular transformation V₁ vertex vertex-set vertices w₁ weighted matroid