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The study paper deals with sensor fault detection problem for a class of linear uncertain systems with bounded disturbances and non-zero constant reference inputs. The sensor faults are modelled as multi-mode, named as fault-free mode and faulty modes. A steady-state-based approach is proposed to detect the sensor faults. The steady-state-based approach can be used to detect lock-in-place sensor faults with arbitrary small magnitudes, which has not been well investigated in the literature. A convergent iterative algorithm based on linear matrix inequalities is given to obtain the solutions. A numerical example is given to illustrate the effectiveness of the proposed methods.