Abstract
This paper focuses on the fault detection problem of 2-D systems described by the Roesser model. To detect faults effectively in the presence of disturbances, a fault detection filter is designed to satisfy a finite-frequency $H_{-}$ index and a finite-frequency $H_\infty $ index simultaneously. The corresponding finite-frequency performance analysis conditions are obtained by the aid of the generalized Kalman–Yakubovich–Popov lemma. Then, convex filter design conditions are derived by constructing a hyperplane tangent combined with linear matrix inequality techniques. An algorithm is proposed to construct a desired fault detection filter. Finally, a numerical example is given to show the effectiveness of the proposed method.
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