A RECURSIVE SCHUR-BASED SOLUTION OF THE 4-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-diagona l inner matrix. Then, using convenient spectral factorizations, we are able to parameterize the unknown entry in terms of a Schur-type matri x function, which is shown to satisfy a finite number of interpolation conditions of the Hermite-Fejer type. AH possible interpolating funct ions are then determined via a simple recursive procedure that constru cts a transmission-line (or lattice) cascade of elementary J-lossless sections. This also leads to a pammeterization of all solutions of the four-block problem in terms of a linear fractional transformation.