Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

Abstract

AbstractIn this paper, the fault detection problem for a class of discrete‐time polytopic uncertain systems is studied. Different from the traditional methods dealing with polytopic uncertainties, not only its values but also the probability distributions are considered. First of all, the above process about polytopic uncertainty is described by applying a Markov process. Then, the original system with polytopic uncertainties becomes to be a Markovian jump system (MJS) without any uncertainty. Accordingly, the fault detection problem is transformed to be a similar one but considered for an MJS. Particularly, the fault detection and isolation (FDI) filter is constructed to be mode‐dependent and also said to be polytope‐dependent. Since more information of uncertainty is considered, it is claimed that the obtained results are less conservative. Finally, a practical example is used to show the effectiveness and superiority of the proposed methods.