Critical-Time Analysis of Cyber-Physical Systems subject to Actuator Attacks and Faults.

A novel quantitative criterion, namely critical time, is investigated to characterize the degree of resilience of controlled cyber-physical systems. Resilience is defined as system's ability to contain the maximal impact of anomalies and recover to a nominal mode. Anomalies are understood as any kind of attack or fault that leads to abnormal behavior of the controlled system. The critical time is the maximal time-horizon for which a system is considered to be safe after the occurrence of an anomaly. An increase of critical time will leave more time for defense mechanisms, including human operators, to detect and mitigate anomalies. While most of the literature focuses on the impact part of resilience, this criterion is tied with the recovery part. In this work, it is shown how the computation of the critical time can be done for discrete-time LTI models. To achieve this, sufficient conditions in the form of iterative LMI-based algorithms are established. A numerical example is provided to illustrate the theoretical results.