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A discrete-time game-theoretic fault detection filter

The fault detection problem is approximated by a discrete-time disturbance attenuation problem which in turn is cast into a discrete minimax problem. Solving the game leads to a Riccati-based filter. As the sampling time decreases the discrete-time filter converges to the continuous-time game-theoretic fault detection filter. As the disturbance attenuation bound is taken to zero, the discrete-time fault detection filter exhibits different properties from its continuous-time counterpart. The solution to the Riccati equation in the limit exists and the nuisance fault direction appears as an invariant direction of the Riccati equation. The Riccati equation in the limit and the detection filter equations are projected orthogonally to the nuisance direction to obtain a reduced-order Riccati and filter equations. The reduced-order estimates remain naturally unbiased when any nuisance fault occurs.