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 |
GraphTheoretic Approach to the Solvability | 28 |
GraphTheoretic Approach to the Controllability | 85 |
Copyright | |
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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 block-triangular blocks C₁ coefficient matrix column-set columns combinatorial canonical form computation consider corresponding decomposition defined deg p(s denote 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 Hasse diagram independent-flow problem Jacobian matrix Japanese layered mixed matrix M-components mathematical matroid-theoretic maximum flow maximum independent flow maximum matching Murota nonsingular nonvanishing entries obtained partial order permutation permutation matrices physical polymatroid polynomial Proof Prop Proposition rank D(z rational numbers representation graph resp respectively row-set signal-flow graph standard form 12.1 strongly connected component structural controllability structural solvability submatrix subproblems subset system of equations term-rank Theorem Trans transformation V₁ vertex vertex-set vertices weighted matroid