Filter design for cyber-physical systems against DoS attacks and unreliable networks: A Markovian approach

This article proposes a novel approach for designing a mode-dependent $H_{\infty }$ full-order dynamic filter for a cyber-physical system (CPS) that is subject to polytopic uncertainties. The CPS operates on an unreliable network that is susceptible to transmission failures and Denial of Service (DoS) attacks. The attackers have limited energy resources, and the duration of the DoS attack is limited to a maximum number of consecutive time instants. The network is modeled after a proposed non-homogeneous Markov chain whose transition probability matrix may feature uncertain and unknown probabilities, which are dependent on time-varying parameters. The design conditions for the filter are obtained using parameter-dependent linear matrix inequalities. The proposed filter is shown to be effective in reducing the impact of DoS attacks and transmission failures on the CPS. Numerical experiments are presented to illustrate the efficacy of the proposed filter design method, demonstrating its ability to mitigate the effects of uncertainties and attacks on the CPS.