Robust Fault Detection Of Jump Systems With Partly Unknown Transition Probabilities

In this paper, Markovian jump systems(MJSs) with uncertainties, delays, nonlinearities and other factors are investigated about their robust fault detection(RFD) problem. At present, reaearch results on MJSs are mostly on the assumption that one can obtain the all transition probabilities. However, in practical systems, the elements in transition probability matrices of MJSs can not be completely obtained or the cost is probably very high. Based on this, RFD problem on MJSs with partly unknown transition probabilities is studied. The main work includes the following aspects:Firstly, RFD problem on generally linear MJSs with partly unknown transition probabilities is studied. RFD observer system is constructed based on the observer method. In the proof processing, free-connection weighting matrices are added to the weak infinitesimal operator of selected Lyapunov function, by which the conservatism of the relevant conclusions is reduced in constract with fixed-connection weighting matrices. A series of linear matrix inequalities(LMIs) which ensure the system’s stochastic asymptotic stability and guarantee the existence of the observer system are given and proved. Furthermore, an optimization design approach is derived and the optimal RFD observer system is obtained finally.Secondly, RFD problem for delay-dependent Markovian jump systems(MJSs) with partly unknown transition probabilities and time-varying delay is investigated. Delay-dependent robust fault detection filter system is constructed on the basis of the filter and free-connection weighting matrix method. Since given conclusion inequalities have nonlinear terms, the improved cone complementary linearisation(ICCL) algorithm is introduced, and then optimal RFD filter is obtained.Thirdly, time-delay nonlinear MJSs with parameter uncertainties are studied. Nonlinear parts of the considered nonlinear Markov jump system are linearized by using gradient linearization approach. Based on the filter and free-connection weighting matrices, local filter gains are obtained. Afterwards, continuous gain-scheduled RFD filter is designed by applying continuous gain-scheduled theory. Some simulation results are obtained to illustrate the RFD filter system can detect the faults shortly and sensitively, and also robustly to parameter uncetainties and external unknown disturbances.