A fault detection and isolation filter design method for Markov jump linear parameter-varying systems

A fault detection and isolation (FDI) filter design method is proposed for linear parameter-varying (LPV) systems, which are subject to abrupt changes in their structure. Such a phenomenon is modeled by a finite state Markov chain whose outcome is supposed to be directly available along with its rates transition matrix. The FDI filter is designed as a bank of ℋ−/ℋ∞ Luenberger observers, derived by optimizing frequency conditions that ensure guaranteed levels of disturbance rejection, fault sensitivity and are capable to discriminate anomalous events belonging to different fault classes. It is proved that, by resorting to stochastic stability concepts, the design method can be recast as a linear matrix inequality programming program in the observer bank gains. The resulting residual generator is a jump parameter-dependent observer jointly exploiting the available measures on the deterministic plant parameter and on the instantaneous Markov chain realization. An FDI threshold logic is also proposed in order to reduce the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example.