On the Output Redundancy of LTI Systems: A Geometric Approach with Application to Privacy
<|reference_start|>On the Output Redundancy of LTI Systems: A Geometric Approach with Application to Privacy: This paper examines the properties of output-redundant systems, that is, systems possessing a larger number of outputs than inputs, through the lenses of the geometric approach of Wonham et al. We begin by formulating a simple output allocation synthesis problem, which involves ``concealing" input information from a malicious eavesdropper having access to the system output, while still allowing for a legitimate user to reconstruct it. It is shown that the solvability of this problem requires the availability of a redundant set of outputs. This very problem is instrumental to unveiling the fundamental geometric properties of output-redundant systems, which form the basis for our subsequent constructions and results. As a direct application, we demonstrate how output allocation can be employed to effectively protect the information of input information from certain output eavesdroppers with guaranteed results.<|reference_end|>
@article{yang2024on,
    title={On the Output Redundancy of LTI Systems: A Geometric Approach with
  Application to Privacy},
    author={Guitao Yang, Alexander J. Gallo, Angelo Barboni, Riccardo M.G.
  Ferrari, Andrea Serrani and Thomas Parisini},
    journal={arXiv preprint arXiv:2409.17705},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.17705},
    primaryClass={eess.SY cs.SY}
}