  Resilient systems are able to recover quickly and easily from disturbed
system states that might result from hazardous events or malicious attacks. In
this paper a novel resilience metric for linear time invariant systems is
proposed: the minimum control energy required to disturb the system is set into
relation to the minimum control energy needed to recover. This definition
extends known disturbance rejection metrics considering random effects to
account for adversarial disturbances. The worst-case disturbance and the
related resilience index can be computed efficiently via solving a generalized
eigenvalue problem that depends on the controllability Gramians of the control
and disturbance inputs. The novel metric allows improving system resilience by
optimizing the restorative control structure or by hardening the system against
specific attack options. The new approach is demonstrated for a coupled
mechanical system.
