Optimal filtering for left invertible linear systems subject to intermittent unknown inputs

This paper presents an optimal filtering of the maximum estimable state in left invertible discrete-time stochastic linear systems subject to intermittent unknown inputs. The use of the obtained filter, expressed as a standard Kalman filter updated online from the intermittent unknown inputs estimate, is illustrated in the area of networked control systems subject to deception attacks on the control signal transmitted by the controller to the plant. Stochastic stability conditions of the filter are established when the arrival sequence of deception attacks follows independent Bernoulli random variables.