Bounding the l<inf>2</inf> sensitivity for positive linear observers

Abstract

We consider the design of differentially private Luenberger observers for positive linear systems. In particular, we derive a bound for the l2 sensitivity of Luenberger observers, which is used to quantify the noise required to achieve relaxed differential privacy via the Gaussian mechanism. An approach to minimise this bound for positive observers is described and several bounds relevant to this problem are derived.