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.