Measuring LTI System Resilience against Adversarial Disturbances based on Efficient Generalized Eigenvalue Computations

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.