Characterising the vulnerability of linear control systems under sensor attacks using a system's security index

We introduce the `security index' of a discrete-time, linear time-invariant system under sensor attacks as a quantitative representation-free measure on the vulnerability of an observable system. Ideas from linear coding theory are employed in providing conditions for attack detection and correction in terms of a system's security index, along with methods for its computation based on different representations of a system. Moreover, we provide conditions under which the security index of a control system can be manipulated via state feedback. Finally, we develop algorithms for attack detection and discuss attack correction.