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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Factorization of non-proper rational matrix functions
verfasst von : Harm Bart, Marinus A. Kaashoek, André C. M. Ran
Erschienen in: A State Space Approach to Canonical Factorization with Applications
Verlag: Birkhäuser Basel
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In this chapter we treat the problem of factorizing a non-proper rational matrix function. The realization used in the earlier chapters is replaced by
$$ V(\lambda ) = I + C(\lambda G - A)^{ - 1} B. $$
Here
I=I
m
is the
m × m
identity matrix,
A
and
G
are square matrices of order
n
say, and the matrices
C
and
B
are of sizes
m × n
and
n × m
, respectively. Any rational
m × m
matrix function
W
, proper or non-proper, admits such a representation. The representation (4.1) allows us to extend the results obtained in the previous chapter to arbitrary rational matrix functions. As an application we treat the problem to invert a singular integral operator with a rational matrix symbol.