Separation Principle with Secure State Estimation and Lyapunov Stability of Cyber-Physical System under Sensor Attack

In Cyber Physical Systems (CPS), sensor outputs are frequently communicated within the system and are thus vulnerable to cyber-attacks by adversaries. If the measurements given to observer are not reliable, then the states are not correctly estimated leading to erroneous state-feedback control input which may result in an undesired system response. Considering a 2m- sparse observable system, one can identify un-attacked sensors, then secure observer uses their measurements only for secure state estimation of a CPS under attack. These securely estimated states are then given as feedback input to controller for obtaining the desired stabilized system response. In this article, separation principle is extended with secure state estimation for feedback and independent LMIs for designing the secure observer and secure- estimated-state feedback gain matrices are derived. Lyapunov stability of the closed loop system is developed with and without delayed feedback.