Fault detection for a class of non-linear networked control systems in the presence of Markov sensors assignment with partially known transition probabilities

In this study, the problem of fault detection for a class of discrete-time non-linear networked control systems is investigated. An event modelled as a Markov chain taking matrix values in a certain set with partially known transition probabilities is utilised to characterise the phenomenon of the sensors assignment. A full-order mode-dependent fault detection filter is constructed and the corresponding fault detection problem is converted into an H_∞ filtering problem of a Markov jump system with partially known transition probabilities. Sufficient conditions for the existence of the fault detection filter are formulated as a linear matrix inequality-based convex optimisation problem. If the convex optimisation problem has a feasible solution, the corresponding fault detection filter parameters are determined. A numerical example with four cases of transition probability matrices is presented to show the usefulness of the developed method.