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.

中文翻译：

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针对尖锐输入异常的风险分析的关键时间指标：计算和应用案例研究

本文研究了关键时间标准，作为受控系统的安全度量，这些受控系统会受到急剧输入异常（攻击、故障）的影响，其特点是在较短的时间内产生高影响（例如拒绝服务、上饱和攻击）。临界时间是指系统在发生异常后可以被认为是安全的最大时间范围。该指标预计对于风险分析和治疗策略（预防、检测、缓解）的离线设计很有价值。在这项工作中，线性系统和几类尖锐输入异常的临界时间计算问题，取决于输入通道和异常信号值的集合，是基于二次约束（QC）框架制定的，其中集合由 QC 不等式和等式的交集表示。然后，提出了一种基于迭代LMI的算法来获得对关键时间的低估，确保系统的安全，直到达到计算的时间。最后，通过几个相关场景，以四联坦克的案例研究来说明和讨论关键时间作为防御设计指标的潜力。