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.

中文翻译：

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正线性观测器问题的一些新颖方面：差分隐私和最佳l ₁灵敏度

我们提出了几个有关正线性观测器的l ₁灵敏度（差分隐私的关键参数）的几个结果。具体来说，对于隔间系统，我们为积极的观察者导出了明确的分析表达式，该表达式最小化了对l ₁灵敏度的限制。给出了单输出系统和多输出系统类别的结果。对于单输出的一般正系统，我们刻画了给定收敛速度下正观测器的最佳l ₁灵敏度范围。我们还对敏感性更强的普通观察者类别进行了初步观察。