Systems Analysis by Graphs and Matroids

This monograph illustrates how engineering problems can be solved using the results of combinatorial mathematics through appropriate mathematical modelling. 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 modellings. The reader should become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach.