Johnson, Russell and Tesi, Alberto:
On the $D$-stability problem for real matrices
Bollettino dell'Unione Matematica Italiana Serie 8 2-B (1999), fasc. n.2, p. 299-314, Unione Matematica Italiana (English)
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Sunto
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 $4 \times 4$
Referenze Bibliografiche
[2]
K.
ARROW
-
M.
MCMANUS
,
A note on dynamic stability,
Econometrica,
26 (
1958), 448-454. |
MR 103767 |
Zbl 0107.37201[3]
C.
BAHL
-
B.
CAIN
,
The inertia of diagonal multiples of $3 \times 3$ real matrices,
Lin. Algebra Appl.,
18 (
1977), 267-280. |
MR 573019 |
Zbl 0379.15004[4]
B.
CAIN
,
Real $3 \times 3$$D$-stable matrices,
J. Res. Nat. Bur. Standards, Sec. B,
80 (
1976), 75-77. |
MR 419478 |
Zbl 0341.15009[5]
D.
CARLSON
,
A class of positive stable matrices,
J. Res. Nat. Bur. Standards, Sec. B,
78 (
1974), 1-2. |
MR 332834 |
Zbl 0281.15020[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 1307123 |
Zbl 0877.93079[7]
A.
ENTHOVEN
-
K.
ARROW
,
A theorem on expectations and the stability of equilibrium,
Econometrica,
24 (
1956), 288-293. |
MR 85963 |
Zbl 0074.15001[9]
M.
FIEDLER
-
V.
PTAK
,
Some generalizations of positive definiteness and monotonicity,
Numerische Mathematike,
9 (
1966), 163-172. |
MR 209309 |
Zbl 0148.25801[10]
B.
GANTMACHER
,
The theory of matrices, Vols. I-II,
Chelsea, New York (
1960). |
Zbl 0927.15001[11]
D.
HERSHKOWITZ
,
Recent directions in matrix stability,
Lin. Algebra Appl.,
171 (
1992), 161-186. |
MR 1165452 |
Zbl 0759.15010[12]
C.
JOHNSON
,
Sufficient conditions for $D$-stability,
J. Economic Theory,
9 (
1974), 53-62. |
MR 463213[13]
H.
KHALIL
-
P.
KOKOTOVIC
,
$D$-stability and multi-parameter singular perturbations,
SIAM J. Cont. Opt.,
17 (
1979), 59-65. |
MR 516856 |
Zbl 0403.93026[15]
A.
SEIDENBERG
,
A new decision method for elementary algebra,
Ann. Math.,
60 (
1954), 365-374. |
MR 63994 |
Zbl 0056.01804