Author | Murota, Kazuo. author |
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Title | Systems Analysis by Graphs and Matroids [electronic resource] : Structural Solvability and Controllability / by Kazuo Murota |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1987 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61586-3 |
Descript | X, 284 p. online resource |
1. Preliminaries -- 1. Convention and Notation -- 2. Algebra -- 3. Graph -- 4. Matroid -- 2. Graph-Theoretic Approach to the Solvability of a System of Equations -- 5. Structural Solvability of a System of Equations -- 6. Representation Graph -- 7. Graphical Conditions for Structural Solvability -- 8. Decompositions of a Graph by Menger-type Linkings -- 9. Decompositions and Reductions of a System of Equations -- 10. Application of the Graphical Technique -- 11. Examples -- 3. Graph-Theoretic Approach to the Controllability of a Dynamical System -- 12. Descriptions of a Dynamical System -- 13. Controllability of a Dynamical System -- 14. Graphical Conditions for Structural Controllability -- 15. Discussions -- 4. Physical Observations for Faithful Formulations -- 16. Mixed Matrix for Modeling Two Kinds of Numbers -- 17. Algebraic Implication of Dimensional Consistency -- 18. Physical Matrix -- 5 Matroid-Theoretic Approach to the Solvability of a System of Equations -- 19. Rank of a Mixed Matrix -- 20. Algorithm for Computing the Rank of a Mixed Matrix -- 21. Matroidal Conditions for Structural Solvability -- 22. Combinatorial Canonical Form of a Layered Mixed Matrix -- 23. Relation to Other Decompositions -- 24. Block-Triangularization of a Mixed Matrix -- 25. Decomposition of a System of Equations -- 26. Miscellaneous Notes -- 6. Matroid-Theoretic Approach to the Controllability of a Dynamical System -- 27. Dynamical Degree of a Dynamical System -- 28. Matroidal Conditions for Structural Controllability -- 29. Algorithm for Testing the Structural Controllability -- 30. Examples -- 31. Discussions -- Conclusion -- References