A Lowner tensorization technique for MIMO transfer function decoupling

We address the problem of finding a diagonal representation of a multi-input-multi-output (MIMO) system in the frequency domain, in other words, decomposing a MIMO system into a set of single-input-single-ouput (SISO) systems as in

G(ωk) = W D(ωk) VT, for k = 1, ..., N,

D(ωk) = diag( s1(ωk), ..., sR(ωk) ).

The procedure is based on recent advances in tensor decomposition and their application in signal processing. Collecting the frequency response matrices over a frequency range naturally leads to a three-dimensional array. Other essential elements are the fact that the transfer function of a linear time-invariant system is a rational function of the frequency variable, and the low-rank property of a Lowner matrix derived from an arbitrary rational function. The approach leads to a third or fourth order Lowner tensorization with a corresponding tensor decomposition to recover the desired decoupled representation. The method is validated on simulation examples, illustrating its effectiveness.


  1. Dieter Verbeke, Mariya Ishteva, Philippe Dreesen. A Lowner tensorization technique for MIMO transfer function decoupling, in preparation, 2019.
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