  Interconnected systems such as power systems and chemical processes are often
required to satisfy safety properties in the presence of faults and attacks.
Verifying safety of these systems, however, is computationally challenging due
to nonlinear dynamics, high dimensionality, and combinatorial number of
possible faults and attacks that can be incurred by the subsystems
interconnected within the network. In this paper, we develop a compositional
resilience index to verify safety properties of interconnected systems under
faults and attacks. The resilience index is a tuple serving the following two
purposes. First, it quantifies how a safety property is impacted when a
subsystem is compromised by faults and attacks. Second, the resilience index
characterizes the needed behavior of a subsystem during normal operations to
ensure safety violations will not occur when future adverse events occur. We
develop a set of sufficient conditions on the dynamics of each subsystem to
satisfy its safety constraint, and leverage these conditions to formulate an
optimization program to compute the resilience index. When multiple subsystems
are interconnected and their resilience indices are given, we show that the
safety constraints of the interconnected system can be efficiently verified by
solving a system of linear inequalities. We demonstrate our developed
resilience index using a numerical case study on chemical reactors connected in
series.
