Actuator fault detection filter design for discrete-time systems with a descriptor system method

In this paper, the problem of fault detection filter design for discrete-time systems is considered. By means of a descriptor system method, this paper designs a fault detection filter such that the residual system is admissible and satisfies the H_∞ performance index when control inputs, actuator faults and unknown bounded disturbances exist. Based on the Lyapunov functional approach, a sufficient condition for the admissibility of the residual system is expressed via linear matrix inequalities and the desired detection filter is obtained. A numerical example is provided to show the feasibility and applicability of the proposed method.