State filtering for discrete-time stochastic linear systems subject to random cyber attacks and losses of measurements

This paper presents a state filtering strategy for network controlled systems subject to cyber attacks assumed to occur when the control signal sent by the controller to the plant is lost. After having represented the hypothesized cyber attacks as intermittent unknown inputs, the state filtering scheme is obtained by designing a modified version of the unknown input Kalman filter restricted, in its original version, to the treatment of permanent unknown inputs. The existence condition of the unknown input Kalman filter is ensured by a secure network for the transmission of measurements directly affected by cyber attacks. The stochastic stability of the state filter is studied when independent Bernoulli processes govern the random arrival of cyber attacks and measurements. A numerical example illustrates the obtained results.