Stabilization of Linear Cyber-Physical Systems Against Attacks via Switching Defense

Abstract

This paper studies cyber-physical systems modeled with linear dynamics subject to attacks on the parameters. The attacker knows at all times the defense employed and injects a destabilizing piecewise Lipschitz time-varying attack signal. The defender does not know the specific attack and aims to preserve system stability. We propose a partitioning strategy for the set of possible attacks that generates a finite collection of candidate defenses such that, for each member of the partition, there is a defense that stabilizes the system with respect to all static attack signals belonging to it. The defender then implements a mechanism that switches among the candidate defenses based on the evaluation of a Lyapunov-based criterion that determines whether the current defense is stabilizing. We characterize the properties of the switched time-varying system with delay, the latter arising from the interval between the switch-triggering events and their actual implementation. Our analysis provides a tolerance on the implementation delay that prevents the defense signal from constantly switching. In addition, we also identify a condition on the switching frequency that ensures global exponential stability. Simulations of the proposed switched defense mechanism illustrate its performance and advantages over static defenses.