Finite-Frequency Fault Detection for Two-Dimensional Roesser Systems

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.