Hostname: page-component-7b7567c8c-2rsb6 Total loading time: 0 Render date: 2026-11-12T08:06:47.039Z Has data issue: false hasContentIssue false
  • English
  • Français

Generic Matrix Sign-Stability

Published online by Cambridge University Press:  20 November 2018

Takeo Yamada
Takeo Yamada*
Affiliation:
Department of Social Sciences National Defense Academy Yokosuka, Kanagawa 239 Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A new concept of generic sign-stability is proposed, and a necessary and sufficient condition for this property is given. This result shows that the condition proposed by Quirk and Ruppert [12] is correct almost everywhere, and helps to clarify the counterexample presented by Jeffries [4].

Keywords

05C5093D20

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987, pp. 370 - 376
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Busucker, R.G. and Saaty, T.L., Finite Graphs and Networks: An Introduction with Applications, McGraw-Hill, New York, 1965.Google Scholar
2. Dieudonné, J., Foundements de l'analyse moderne, Gauthier-Villars, Paris, 1960.Google Scholar
3. Ishida, Y., Adachi, N. and Tokumaru, H., Some results on the quantitative theory of matrix, Trans, of the Society of Instrument and Control Engineers, Japan, 17 (1981), pp. 49—55.Google Scholar
4. Jeffries, C., Qualitative stability and digraphs in model ecosystems, Ecology, 55 (1974), pp. 1415–1419.Google Scholar
5. Jeffries, C., Klee, V. and Van den Driessche, P., When is a matrix sign stable? Canadian J. of Mathematics 29 (1977), pp. 315–326.Google Scholar
6. Kendig, K., Elementary Algebraic Geometry, Springer, New York, 1977.Google Scholar
7. Lin, C.T., Structural Controllability, IEEE Trans. Automat. Contr. AC-19 (1974), pp. 201–208.Google Scholar
8. Luenberger, D.G., Introduction to Dynamic Systems: Theory, Models and Applications, John Wiley and Sons, New York, 1979.Google Scholar
9. Maybee, J. and Quirk, J., Qualitative problems in matrix theory, SIAM Review 11 (1969), pp. 30—51.Google Scholar
10. Mayeda, H., On structural controllability theorem, IEEE Trans. Automat. Contr. AC-26 (1981), pp. 795–798.Google Scholar
11. Ore, O., Theory of Graphs, American Math. Society , Providence, 1962.Google Scholar
12. Quirk, J. and Ruppert, R., Qualitative economics and stability of equilibrium, Review of Economic Studies 32 (1965), pp. 311–326.Google Scholar
13. Wonham, W.M., Linear Multivariable Control: A Geometric Approach, Springer-Verlag, New York, 1974.Google Scholar