MIMO frequency domain system identification for discrete systems

In this paper, we propose a two-stage algorithm utilizing the Cauchy integral and the matrix-valued adaptive Fourier decomposition (abbreviated as matrix AFD) to identify transfer functions of discrete linear time-invariant (LTI) multi-input multi-output (MIMO) systems. The maximal selection principle defined in matrix AFD involves the selection of the parameter pair
$(a,\ P)$
where
$a$
is a point in the unit disk on the complex plane and
$P$
is an orthogonal projection. The optimal selection of
$P$
is shown to be dependent on the previously fixed
$a$
, which means we reduce the computation complexity to search the optimal parameter pair
$(a,\ P)$
. With some numerical experiments we show that the proposed algorithm is effective in both the noise-free and noised cases.