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This paper investigates the critical-time criteria as a security metric forcontrolled systems subject to sharp input anomalies (attack, fault),characterized by having high impact in a reduced amount of time (e.g.denial-of-service, attack by upper saturation). The critical-time is themaximal time-horizon for which a system can be considered to be safe after theoccurrence of an anomaly. This metric is expected to be useful for riskanalysis and treatment (prevention, detection, mitigation). In this work, thecomputational problem of the critical-time for uncertain linear systems andseveral classes of sharp input anomalies, depending on the input channel andthe set of abnormal signal values, is formulated based on the quadraticconstraints (QC) framework, representing sets by the intersection of QCinequalities and equalities. An iterative LMI-based algorithm is then proposedto provide an under-estimate of the critical-time. Finally, the potential ofthe critical-time as a metric for defense design is illustrated and discussedon the quadruple-tank case study through different relevant scenarios.

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