On the Hermite-Fujiwara theorem in stability theory
Author:
R. E. Kalman
Journal:
Quart. Appl. Math. 23 (1965), 279-282
MSC:
Primary 30.10
DOI:
https://doi.org/10.1090/qam/190299
MathSciNet review:
190299
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References |
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Additional Information
J. R. Ragazzini and G. F. Franklin, Sampled-data control systems, McGraw-Hill, N. Y., 1958
- Matsusaburô Fujiwara, Über die algebraischen Gleichungen, deren Wurzeln in einem Kreise oder in einer Halbebene liegen, Math. Z. 24 (1926), no. 1, 161–169 (German). MR 1544753, DOI https://doi.org/10.1007/BF01216772
C. Hermite, Sur le nombre des racines d’une équation algèbrique comprises entre des limites donées, Oeuvres 1, 397–114
- A. Cohn, Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z. 14 (1922), no. 1, 110–148 (German). MR 1544543, DOI https://doi.org/10.1007/BF01215894
- R. E. Kalman and J. E. Bertram, Control system analysis and design via the “second method” of Lyapunov. II. Discrete-time systems, Trans. ASME Ser. D. J. Basic Engrg. 82 (1960), 394–400. MR 157811
P. C. Parks, Lyapunov and the Schur-Cohn stability criterion, IEEE Trans, on Automatic Control 8 (1964) 121
- Morris Marden, The Geometry of the Zeros of a Polynomial in a Complex Variable, Mathematical Surveys, No. 3, American Mathematical Society, New York, N. Y., 1949. MR 0031114
- Olga Taussky, Matrices $C$ with $C^{n}\rightarrow 0$, J. Algebra 1 (1964), 5–10. MR 161865, DOI https://doi.org/10.1016/0021-8693%2864%2990003-1
- R. E. Kalman, Mathematical description of linear dynamical systems, J. SIAM Control Ser. A 1 (1963), 152–192 (1963). MR 0152167
R. E. Kalman, On the stability of a polynomial, to appear
J. R. Ragazzini and G. F. Franklin, Sampled-data control systems, McGraw-Hill, N. Y., 1958
M. Fujiwara, Über die algebraischen Gleichungen, deren Wurzeln in einem Kreise oder in einer Halbebene liegen, Math. Z. 24 (1926) 160–169
C. Hermite, Sur le nombre des racines d’une équation algèbrique comprises entre des limites donées, Oeuvres 1, 397–114
A. Cohn, Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z. 14 (1922) 110–148
R. E. Kalman and J. E. Bertram, Control system analysis and design via the ’second method’ of Lyapunov. II. Discrete-time systems. J. Basic Engr. (Trans. ASME) 82 $D$ (1960) 394–399
P. C. Parks, Lyapunov and the Schur-Cohn stability criterion, IEEE Trans, on Automatic Control 8 (1964) 121
M. Marden, The geometry of the zero of a polynomial in a complex variable, Chapter X, Am. Math Soc., 1949.
Olga Taussky, Matrices $C$ with ${C^n} \to 0$, J. Algebra, 1 (1964) 5–10
R. E. Kalman, Mathematical description of linear dynamical systems, J. Control (SIAM) 1 (1963) 152–192
R. E. Kalman, On the stability of a polynomial, to appear
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Article copyright:
© Copyright 1965
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