A Fault Detection filter design method for Markov Jump Linear Parameter Varying Systems

In this paper, a fault detection (FD) 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 states Markov chain whose outcome is supposed to be directly available along with its rate transition matrix. The FD Filter is designed as a bank of H∞ Luenberger observers, derived by optimizing frequency conditions which ensure guaranteed level of disturbance rejection and fault sensitivity. It is proved that, resorting to stochastic stability concepts, the design method can be recast as a Linear Matrix Inequality (LMI) program in the observer bank gains. The resulting residual generator is a jump parameter dependent observer and exploits jointly the deterministic plant parameter knowledge and the instantaneous Markov chain realization. A FD threshold logic is proposed in order to reduce the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example.