Fault detection filter for discrete piecewise linear systems

This paper presents the fault detection problem for a class of discrete-time piecewise linear systems with external disturbances. It is shown that the stability of the system can be established, moreover, the possible faults can be detected and the external disturbances can be filtered out. In this paper, the H ∞ performance of the stability is guaranteed with a prescribed attenuation level γ and the sensitivity of the residual to the fault is enhanced by means of a maximized H ∞ norm β. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially available software. At last, a simulation example is given to illustrate the performance of the proposed approaches.