State space model identification: from unstructured to structured models with an H∞ approach

Subspace model identification algorithms have become extremely popular in the last few years thanks to the ease with which they can provide consistent estimates for MIMO state space models in a non iterative way, exploiting a full parameterisation of the system matrices. The only, well known, downside of this approach is the impossibility to impose a fixed basis to the state space representation, and therefore the difficulties in recovering physically-motivated models. The problem considered in this paper is the one of recovering the numerical values of the physical parameters of a structured representation of the system starting from a fully parameterised identified model. It will be shown that this can be achieved without explicitly constructing the similarity transformation, for linear time-invariant systems, linear time-periodic systems and linear parameter-varying systems identified from a periodic scheduling sequence. Two numerical examples are presented to illustrate the approach.