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stability. However, the authors also specified that resilience postulates flexibility in terms of performance,
structure and function while these changes are not irreversible or unacceptable.

Resilience is also defined as the maintenance of “state awareness and an accepted level of operational nor-
malcy in response to disturbances” [16] . Operational normalcy corresponds to the maintenance of “stability
and integrity of core processes” according to McDonald [17] and resilience was described by Wreathall [18] as
the ability to “keep, or recover quickly to, a stable state”. These definitions confirm the previous description as
resilience focuses on some operational stability even if systems are supposed to “tolerate fluctuations via their
structure, design parameters, control structure and control parameters” [19] . A new point highlighted by this
definition is the need to collect and fusion data concerning the current state of the system. This knowledge
aims at knowing the current date of the system and its environment and is a basis for decisions [18] . Processes
to collect, fuse, and prioritize information should be considered when designing resilient systems. Indeed, re-
silient systems should not be considered as a single technology but as a complex integrated system of systems
that ensures coordination among subsystems through communication and sharing of information [20] .

2.2. Resilience is related to service delivery
Sterbenz et al. [21] considered systems as networks, and their resilience is defined as the ability “to provide
and maintain an acceptable level of service in face of various faults and challenges to normal operation”. This
definition is close to another one given by Laprie [22] , where resilience is “the persistence of service delivery
that can justifiably be trusted, when facing changes”. For both definitions, resilience focuses on service delivery
and particularly on avoidance of service failure. System services are the system behavior as it is perceived by
its users [23] . They are different from system functions which correspond to the expected result of the system
behavior, in other words what the system is intended to do. Delving into a more specific domain of cyber-
physical system, Clark and Zonouz [24] defined resilience as the “maintenance of the core [. . .] set of crucial
sub-functionalities despite adversarial misbehaviors” and a guarantee of “recovery of the normal operation
of the affected sub-functionalities within a predefined cost-limit”. Again, this definition reinforces the need
to maintain a service delivery above a fixed threshold. If a perturbation leads the system to be under this
threshold, then the system is in an unacceptable state and has failed to be resilient.

Power systems are also considered [25] , and resilience is defined as the “ability to maintain continuous elec-
tricity flow to customers given a certain load prioritization scheme”. According to the authors, traditional
risk assessment is not the best approach to achieve resilience as resilience concerns “unexpected rare extreme
failures” whose likelihood cannot be easily estimated. Thus, this definition completes the previous ones as it
focuses on service delivery and underlines that some services are more critical than others and should not be
interrupted.

2.3. Events handling
A commonly accepted definition of resilience was given by Vugrin et al. [26] . Resilience is described as the
ability of a system, for a given disruptive event, to “reduce ‘efficiently’ both the magnitude and the duration
of the deviation from targeted ‘system performance’ levels”. This definition has frequently been used to pro-
pose resilience metrics based on system performance such as some metrics detailed in Sections 4.1 and 4.2.
This definition and its derived metrics also imply that a system has different levels of resilience to different
disruptions and an evaluation of resilience is needed for every specific disruption.

Ayyub’s definition of resilience is close to the previous one [27] , as resilience is said to be “the ability to prepare
for and adapt to changing conditions and withstand and recover rapidly from disruptions”. On the contrary
of the previous definition, resilience is not only concerned with the occurrence of disruptions, but is also
considered in a pre-disruption phase as a need for preparation and evolution is pointed out by this definition.