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This paper investigates the problem of fault detection for 2-D systems with lock-in-place sensor faults. Our attention is focused on detecting sensor faults in the presence of disturbances. To this end, a fault detection filter is designed, through which a residual signal is generated for both the fault-free and faulty cases. In light of the generalized Kalman-Yakubovich-Popov lemma for 2-D systems and matrix inequality techniques, convex filter design conditions are derived. Based on these conditions, an algorithm is proposed to calculate the parameters of a desired fault detection filter. Moreover, a residual evaluation function and a threshold are proposed for 2-D systems. Finally, an example is employed to illustrate the effectiveness of the proposed fault detection method.