Redundancy design of networked control systems under denial-of-service attacks

In this paper, we propose a stability assessment method for networked control systems (NCSs) with redundancy design under denial-of-service (DoS) attacks. By modeling the NCS under DoS attacks as a randomly switched system with two modes, we first argue that when redundancy design is considered, assuming gamma distribution for the sojourn time of online mode better reveals the interactions between attacks, auto-correction and offline repairing. To analyze stability of such systems, we appeal to a more general class of randomly impulsive switched systems, whose moment of state is related to the output of an auxiliary linear time-invariant system. We therefore propose criteria for asymptotic moment stability, based on Hurwitzness of the auxiliary system matrix. Finally, we validate the results for an NCS under DoS attacks through numerical simulations, confirming that assuming sojourn times to obey a gamma distribution rather than an exponential distribution leads to less conservative redundancy design.