Models for attack detection and privacy preservation of linear systems can be formulated in terms of their input observability, which is also called the left invertibility of their transfer function matrices. While left invertibility is a classical concept, we re-examine it from the perspectives of security and privacy. In this paper, for discrete-time linear systems, we design an input observer in order to detect attacks. We also present the input observability Gramian, which is used to characterize the systems' privacy level; it is shown that a strong connection can be made between the input observability Gramian and a standard privacy concept called differential privacy.
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