Data-informativity conditions for structured linear systems with implications for dynamic networks
<|reference_start|>Data-informativity conditions for structured linear systems with implications for dynamic networks: When estimating models of of a multivariable dynamic system, a typical condition for consistency is to require the input signals to be persistently exciting, which is guaranteed if the input spectrum is positive definite for a sufficient number of frequencies. In this paper it is investigated how such a condition can be relaxed by exploiting prior structural information on the multivariable system, such as structural zero elements in the transfer matrix or entries that are a priori known and therefore not parametrized. It is shown that in particular situations the data-informativity condition can be decomposed into different MISO (multiple input single output) situations, leading to relaxed conditions for the MIMO (multiple input multiple output) model. When estimating a single module in a linear dynamic network, the data-informativity conditions can generically be formulated as path-based conditions on the graph of the network. The new relaxed conditions for data-informativity will then also lead to relaxed path-based conditions on the network graph. Additionally the new expressions are shown to be closely related to earlier derived conditions for (generic) single module identifiability.<|reference_end|>
@article{hof2024data-informativity,
    title={Data-informativity conditions for structured linear systems with
  implications for dynamic networks},
    author={Paul M.J. Van den Hof, Shengling Shi, Stefanie J.M. Fonken, Karthik R.
  Ramaswamy, Hr{a}kan Hjalmarsson and Arne G. Dankers},
    journal={arXiv preprint arXiv:2409.03883},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03883},
    primaryClass={eess.SY cs.SY}
}