In this contribution, problems related to fault detection filter (FDF) design for uncertain discrete-time systems with both modelling errors and unknown input are studied. The basic idea of our study consists in the formulation of designing robust fault detection filters as a standard H_∞-model matching problem. To this end, the design scheme consists of two parts. We first propose an optimization approach to the design of fault detection filters for the discrete-time systems only with unknown inputs. The resulted fault detection filter acts then as a reference model. In the second part, the design problem is formulated as a standard H_∞-model matching problem which is solved using H_∞-optimization LMI techniques. A numerical example is finally presented to illustrate the developed approach.