Fault detection filter design for discrete-time nonlinear systems— A mixed optimization

This work investigates the problem of designing a fault detection filter for discrete-time nonlinear systems using ℋ − / ℋ ∞ -optimization that simultaneously improves robustness against disturbances and enhances sensitivity to faults. Sufficient conditions for the solvability of this problem are provided in the form of a pair of coupled Hamilton–Jacobi inequalities. Both the finite-horizon and the infinite-horizon problems are addressed. The proposed methodology is elaborated through a couple of examples.