Geodesic
On the $D$-stability problem for real matrices
Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 2, pp. 299-314.

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Vengono discusse delle condizioni sufficienti affinchè una matrice reale $A$ delle dimensioni $n \times n$ sia diagonalmente (o $D$-) stabile. Esse includono delle ipotesi geometriche (condizioni degli ortanti), e un criterio che generalizza un criterio di Carlson. Inoltre si discute la $D$-stabilità robusta per le matrici reali delle dimensioni $4 \times 4$ 
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Johnson, Russell; Tesi, Alberto. On the $D$-stability problem for real matrices. Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 2, pp. 299-314. http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_2_a5/

[1] E. H. Abed , Strong $D$-stability, Syst. Contr. Lett., 7 (1986), 207-212. | MR | Zbl

[2] K. Arrow - M. Mcmanus , A note on dynamic stability, Econometrica, 26 (1958), 448-454. | MR | Zbl

[3] C. Bahl - B. Cain , The inertia of diagonal multiples of $3 \times 3$ real matrices, Lin. Algebra Appl., 18 (1977), 267-280. | MR | Zbl

[4] B. Cain , Real $3 \times 3$$D$-stable matrices, J. Res. Nat. Bur. Standards, Sec. B, 80 (1976), 75-77. | MR | Zbl

[5] D. Carlson , A class of positive stable matrices, J. Res. Nat. Bur. Standards, Sec. B, 78 (1974), 1-2. | MR | Zbl

[6] J. Chen - M. K. H. Fan - C.-C. Yu , On $D$-stability and structured singular values, Sys. Cont. Lett., 24 (1995), 19-24. | MR | Zbl

[7] A. Enthoven - K. Arrow , A theorem on expectations and the stability of equilibrium, Econometrica, 24 (1956), 288-293. | MR | Zbl

[8] M. Fiedler - V. Ptak , On matrices with non-positive off-diagonal elements and positive principal minors, Czech. Math. J., 12 (1962), 382-400. | fulltext mini-dml | MR | Zbl

[9] M. Fiedler - V. Ptak , Some generalizations of positive definiteness and monotonicity, Numerische Mathematike, 9 (1966), 163-172. | MR | Zbl

[10] B. Gantmacher , The theory of matrices, Vols. I-II, Chelsea, New York (1960). | Zbl

[11] D. Hershkowitz , Recent directions in matrix stability, Lin. Algebra Appl., 171 (1992), 161-186. | MR | Zbl

[12] C. Johnson , Sufficient conditions for $D$-stability, J. Economic Theory, 9 (1974), 53-62. | MR

[13] H. Khalil - P. Kokotovic , $D$-stability and multi-parameter singular perturbations, SIAM J. Cont. Opt., 17 (1979), 59-65. | MR | Zbl

[14] S. Lang , Algebra, Addison-Welsey, Reading, Mass., 1965. | MR | Zbl

[15] A. Seidenberg , A new decision method for elementary algebra, Ann. Math., 60 (1954), 365-374. | MR | Zbl