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Keywords
(5)
Invariant Subspace
Minimal Realization
Point of View
State Space
Transfer Function
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Zero/pole structure of linear transfer functions
Zero/pole structure of linear transfer functions,10.1109/CDC.1985.268498,G. Conte,A. M. Perdon,B. F. Wyman
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Zero/pole structure of linear transfer functions
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Citations: 1
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G. Conte
,
A. M. Perdon
,
B. F. Wyman
This paper studies the relationship between the zeros and poles of a linear
transfer function
from a moduletheoretic point of view. The situation is wellunderstood when G(z) is proper, so that the pole module at infinity vanishes and (as always) the polynomial pole module X serves as the
state space
of the
minimal realization
(X;A,B,C) of G(z). There are isomorphisms identifying the (polynomial) zero module Z(G) with V*, the maximum (A,B)invariant subspace of X contained in ker C, and the infinite zero module Z¿ (G) with S*, the minimum conditionally
invariant subspace
of X containing im B [1,2,7]. Our results here show that these two facts can be unified by using exact sequences which require no properness assumptions on G(z).
Conference:
Conference on Decision and Control  CDC
, 1985
DOI:
10.1109/CDC.1985.268498
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Citation Context
(1)
...We will not develop here a complete treatement of the case of poles and zeros at infinity (see [4,6,7,9,
10
,26] for applications), but we will simply point out its general lines, assuming that the reader is familiar with the classical notions...
G. Conte
,
et al.
Zeros, poles and modules in linear system theory
References
(5)
Infinite zero module and infinite pole module
(
Citations: 13
)
G. Conte
,
A. Perdon
Controlled invariance in systems over rings
(
Citations: 19
)
M. L. J. Hautus
Published in 1982.
Strictly Observable Linear Systems
(
Citations: 2
)
Jacob Hammer
,
Michael Heymann
Journal:
Siam Journal on Control and Optimization  SIAM J CONTR OPTIMIZAT
, vol. 21, no. 1, 1983
The zero module and essential inverse systems
(
Citations: 22
)
BOSTWICK F. WYMAN
,
MICHAEL K. SAIN
Journal:
IEEE Transactions on Circuits and Systems
, vol. 28, no. 2, pp. 112126, 1981
On the zeros of a minimal realization
(
Citations: 10
)
B Wyman
Journal:
Linear Algebra and Its Applications  LINEAR ALGEBRA APPL
, vol. 50, no. 1, pp. 621637, 1983
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Citations
(1)
Zeros, poles and modules in linear system theory
G. Conte
,
A. Perdon