On the Output Redundancy of LTI Systems: A Geometric Approach With Application to Privacy

This article 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.