Distributed H_∞ filtering of replay attacks over sensor networks

A distributed H_∞ filtering issue is addressed in this paper for discrete-time nonlinear systems in the face of replay attacks over sensor networks, where an indicator variable is introduced to describe whether a replay attack is launched by the adversaries. First, an interesting pattern dependent on three parameters including a time-varying one is established to account for the temporal behavior of malicious attacks. Then, taking advantage of such a model, the resulting filter dynamic is transformed into a switching system with a subsystem with time-varying delays. By means of the famous switching system theory, a sufficient condition guaranteeing the H_∞ performance is derived to disclose the tolerant attack condition, that is, the attack-active duration and proportion. In addition, the applicable filter gains are achieved with the aid of the solutions of matrix inequalities. Finally, an example is purposively given to adequately illustrate the availability of the developed secure filtering strategy.