Fault detection for linear discrete-time systems with output quantisation

This paper is concerned with the problem of fault detection for a class of linear discrete-time quantised feedback systems, and system outputs are, respectively, quantised by a uniform quantiser and a non-uniform quantiser. A novel unified method is proposed to deal with the two different types of quantisation errors, i.e. the quantisation errors are considered as unknown inputs of the residual generator. Then, an optimal residual generator is constructed to guarantee a suitable trade-off between the sensitivity to faults and the robustness against disturbances as well as quantisation errors. In order to detect the occurrence of faults, the generated residual signal is evaluated, and then two different thresholds based on the stochastic properties of quantisation errors are designed for these two quantisers. In addition, the false alarm rate is introduced to evaluate the fault detection performance. Finally, two examples are given to illustrate the feasibility of the proposed approach.