Systems Analysis by Graphs and Matroids

1. Front Matter

   Pages I-IX

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2. Introduction

   • Kazuo Murota

   Pages 1-4

3. Preliminaries

   • Kazuo Murota

   Pages 5-27

4. Graph-Theoretic Approach to the Solvability of a System of Equations

   • Kazuo Murota

   Pages 28-84

5. Graph-Theoretic Approach to the Controllability of a Dynamical System

   • Kazuo Murota

   Pages 85-121

6. Physical Observations for Faithful Formulations

   • Kazuo Murota

   Pages 122-148

7. Matroid-Theoretic Approach to the Solvability of a System of Equations

   • Kazuo Murota

   Pages 149-224

8. Matroid-Theoretic Approach to the Controllability of a Dynamical System

   • Kazuo Murota

   Pages 225-260

9. Conclusion

   • Kazuo Murota

   Pages 261-262

10. Back Matter

    Pages 263-281

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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 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.

• calculus
• differential equation
• mathematical modeling
• modeling
• system
• combinatorics

• Department of Mathematical Engineering and Instrumentation Physics Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, Japan

  Kazuo Murota

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