Security Index of Linear Cyber-Physical Systems: A Geometric Perspective

This paper is mainly concerned with developing security indices for linear cyber-physical systems (CPS). The approaches for computing security (and consequently vulnerability analysis) of CPS in the literature are based on algebraic methods and system matrices. In this paper, for the first time in the literature we formally address the security index analysis and computation from a geometric system theory perspective. This point of view enables one to develop an algorithm for computing an upper bound on the security index having a linear time complexity with respect to dimension of the system (i.e., $O(n)$). This is a significant improvement compared to the currently available approaches in the literature that have polynomial time complexity. Unlike the approaches in the literature our methodology does not need any restriction on the representation of the system. Moreover, the geometric approach provides a tool to formally analyze the attack signals injected to the CPS by introducing a new type of attack that is more sophisticated than zero dynamic attacks. Finally, we illustrate our proposed methodology through a numerical example.