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

TL;DR

This paper explores the geometric properties of output-redundant LTI systems, focusing on output allocation for input privacy, and demonstrates how redundancy can be used to protect input information from eavesdroppers.

Contribution

It introduces a geometric framework for analyzing output redundancy in LTI systems and applies it to design output allocation strategies for input privacy protection.

Findings

Redundant outputs enable input concealment from eavesdroppers.

A geometric approach characterizes the conditions for output allocation.

Output allocation can effectively protect input information in LTI systems.

Abstract

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.