On the Output Redundancy of LTI Systems
A Geometric Approach With Application to Privacy
Guitao Yang (Loughborough University)
A.J. Gallo (Politecnico di Milano)
Angelo Barboni (Zurich Insurance Group)
Riccardo M.G. Ferrari (TU Delft - Team Riccardo Ferrari)
Andrea Serrani (University of Bologna)
Thomas Parisini (University of Trieste, Imperial College London, Aalborg University)
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Abstract
This paper examines the properties of output-redundant systems, that is, systems possessing a larger number of outputs than inputs, through the lense 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 input information from certain output eavesdroppers with guaranteed results.
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