Some novel aspects of the positive linear observer problem: differential privacy and optimal l1 sensitivity

Abstract

We present several results concerning the l1 sensitivity, a crucial parameter for differential privacy, of a positive linear observer. Specifically, for compartmental systems we derive explicit analytic expressions for positive observers that minimize a bound for the l1 sensitivity. Results are given for single-output systems and classes of multiple-output systems. For single-output general positive systems, we characterize the optimal l1 sensitivity bound of a positive observer with given convergence rate. We also make some initial observations on sensitivity for more general classes of positive observers.