fault detection with randomly occurring nonlinearities and channel fadings

In this paper, the H∞ fault detection problem is investigated for a class of discrete-time stochastic systems with both channel fadings and randomly occurring nonlinearities. Due to Doppler effect and multi-path delays, channel fadings are inevitable and also cause unpredictable dynamic behaviour. The Lth Rice fadings model, which is accounted for both channel fadings and time delays, can be employed to describe this phenomenon. Meanwhile, by using a Bernoulli distributed white sequence, a kind of non-linear disturbance appearing in a random way is also considered in the H∞ fault detection issue. The purpose of the addressed problem is to design a fault detection filter such that, in the presence of channel fadings, the overall fault detection dynamics is stochastically stable and, at the same time, the error between the residual (generated by the fault detection filter) and the fault signal is made as small as possible. By utilising the Lyapunov stability theory associated with the intensive stochastic analysis techniques, sufficient conditions are established under which the addressed H∞ fault detection problem is recast as solving a convex optimisation problem via the semi-definite programme method. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.