MIMO transfer function decoupling by Loewner tensorization

Dynamic systems often have an underlying latent structure that is desirable to uncover during a modeling step or to exploit in applications. Here, we consider MIMO systems that admit a diagonal (or dyadic) form in which the system dynamics are contained in a structure of internal SISO systems surrounded by static mixing matrices that relate the internal dynamics to the inputs and outputs. The fact that linear dynamic systems are described by rational transfer functions naturally leads to a Loewner-based tensor method in which the latent structure is identified by means of a block-term decomposition of a fourth-order tensor built from Loewner matrices constructed from the MIMO input-output data. Numerical experiments illustrate how the proposed decoupling method improves the state-of-the-art approach in terms of guaranteed conditions for the unique retrieval of the structure, and exhibit an improved ability to reject noise.