A recursive Schur-based solution of the four-block problem

We describe a new solution to the four-block problem using the method of generalized Schur analysis. We first reduce the general problem to a simpler one by invoking a coprime factorization with a block-diagonal inner matrix. Then, using convenient spectral factorizations, we are able to parameterize the unknown entry in terms of a Schur-type matrix function, which is shown to satisfy a finite number of interpolation conditions of the Hermite-Fejer type. All possible interpolating functions are then determined via a simple recursive procedure that constructs a transmission-line (or lattice) cascade of elementary J-lossless sections. This also leads to a parameterization of all solutions of the four-block problem in terms of a linear fractional transformation.


Published in:
IEEE Transactions on Automatic Control, 39, 7, 1476-1481
Year:
1994
Publisher:
IEEE
ISSN:
0018-9286
Laboratories:




 Record created 2017-12-19, last modified 2018-12-03


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