Fault Detection for Linear Discrete Time‐varying Systems with Intermittent Observations and Quantization Errors

Abstract

AbstractThis paper deals with the fault detection (FD) problem for linear discrete time‐varying (LDTV) systems subject to multiple intermittent observations and quantization errors. A set of independent identical distributed random variables are introduced as the indicators of the observation sequences to describe the multiple intermittent measurements. The measured observation is quantized by a logarithmic type quantizer. Our focus is to construct an observer‐based fault detection filter (FDF) to recognize the fault in spite of multiple measurement packet dropouts and quantization inaccuracy. By defining generalized input‐to‐output operators, the FD problem is formulated into a two‐objective optimization framework such that stochastic H∞/H∞ or H−/H∞ performance index is maximized. Probability/indicators‐dependent and probability‐dependent analytical solutions are respectively derived by virtue of an adjoint operator based optimization approach for two cases. One is that the indicators are on‐line known while the other one is that the indicators are not available at each time instant. An illustrative example is employed to demonstrate the effectiveness and applicability of the proposed approach.