Generic Matrix Sign-Stability
Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 370-376

Voir la notice de l'article provenant de la source Cambridge University Press

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].
DOI : 10.4153/CMB-1987-054-5
Mots-clés : 05C50, 93D20
Yamada, Takeo. Generic Matrix Sign-Stability. Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 370-376. doi: 10.4153/CMB-1987-054-5
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[1] 1. Busucker, R.G. and Saaty, T.L., Finite Graphs and Networks: An Introduction with Applications, McGraw-Hill, New York, 1965. Google Scholar

[2] 2. Dieudonné, J., Foundements de l'analyse moderne, Gauthier-Villars, Paris, 1960. Google Scholar

[3] 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] 4. Jeffries, C., Qualitative stability and digraphs in model ecosystems, Ecology, 55 (1974), pp. 1415–1419. Google Scholar

[5] 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] 6. Kendig, K., Elementary Algebraic Geometry, Springer, New York, 1977. Google Scholar

[7] 7. Lin, C.T., Structural Controllability, IEEE Trans. Automat. Contr. AC-19 (1974), pp. 201–208. Google Scholar

[8] 8. Luenberger, D.G., Introduction to Dynamic Systems: Theory, Models and Applications, John Wiley and Sons, New York, 1979. Google Scholar

[9] 9. Maybee, J. and Quirk, J., Qualitative problems in matrix theory, SIAM Review 11 (1969), pp. 30—51. Google Scholar

[10] 10. Mayeda, H., On structural controllability theorem, IEEE Trans. Automat. Contr. AC-26 (1981), pp. 795–798. Google Scholar

[11] 11. Ore, O., Theory of Graphs, American Math. Society , Providence, 1962. Google Scholar

[12] 12. Quirk, J. and Ruppert, R., Qualitative economics and stability of equilibrium, Review of Economic Studies 32 (1965), pp. 311–326. Google Scholar

[13] 13. Wonham, W.M., Linear Multivariable Control: A Geometric Approach, Springer-Verlag, New York, 1974. Google Scholar

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