Fault detection for discrete systems based on a descriptor system method

In this study, the problem of fault detection for discrete systems is considered. For control inputs, unknown bounded disturbances and sensor faults, an observer-based fault detection filter is designed based on a descriptor system method such that the error dynamic system is convergent, the effect of the disturbances on the residuals satisfies the H_∞ performance index and the effect of the faults on the residuals satisfies the H_- performance index. By a Lyapunov functional approach, a sufficient condition for the solvability of the fault detection problem is expressed in terms of linear matrix inequalities. A numerical example shows the effectiveness of the proposed method.