Design of robust nonfragile fault detection filter for uncertain dynamic systems with quantization

This paper investigates the fault detection problem for uncertain linear systems with respect to signal quantization. The measurement output transmitted via the digital communication link is considered to be quantized by a dynamic quantizer. Moreover, different from most of existing results on fault detection where the residual generator is assumed to be realized perfectly as the designed one, this study takes the inaccuracy and uncertainty on the implementation of residual generator into account. This paper pays much attention to designing a fault detection filter with quantization as the residual generator and formulates the design problem into the H∞ framework. The objective is to guarantee the asymptotical stability and prescribed performance of the residual system. The S-procedure and a two-step approach are adopted to handle the effects of quantization and uncertainties on residual system. Corresponding design conditions of a robust fault detection filter and a robust nonfragile ones are derived in the form of linear matrix inequalities. Finally, the efficiency of the theoretical results is illustrated by the numerical example.