Critical-time metric for risk analysis against sharp input anomalies: Computation and application case study

This paper investigates the critical-time criteria as a security metric for controlled systems subject to sharp input anomalies (attacks, faults), characterized by high impact in a reduced amount of time (e.g. denial-of-service, upper saturation attack). The critical-time is the maximum time horizon for which a system can be considered to be safe after the occurrence of an anomaly. This metric is expected to be valuable for risk analysis and for the off-line design of a treatment strategy (prevention, detection, mitigation). In this work, the computational problem of the critical-time for linear systems and several classes of sharp input anomalies, depending on the input channel and the set of abnormal signal values, is formulated based on the Quadratic Constraints (QC) framework, where sets are represented by the intersection of QC inequalities and equalities. Then, an iterative LMI-based algorithm is proposed to obtain an underestimation of the critical-time, ensuring the safety of the system until the calculated time is reached. Finally, the potential of critical-time as a metric for defense design is illustrated and discussed on the case study of the quadruple tank through several relevant scenarios.