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For the fault detection filter design of linear time-invariant systems, we propose a novel problem formulation, which not only makes a tradeoff between fault sensitivity and disturbance sensitivity, but also incorporates partial fault decoupling and disturbance decoupling. This formulation compensates the drawbacks of the available frameworks such as ${\cal H}_{-}/{\cal H}_{\infty}$, ${\cal H}_{2}/{\cal H}_{\infty}$...
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