Multiple actuator-fault detectability analysis using invariant sets for discrete-time LPV systems

This paper characterises and analyses the minimum detectable fault (MDF) (named generalised MDF here) for multiple multiplicative actuator faults based on set-separation constraints of healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded inputs and uncertainties. First, multiple multiplicative actuator faults are equivalently transformed into the form of multiple additive actuator faults for the sake of obtaining the simplified faulty residual set explicitly. Then, two different generalised MDF for different multiple actuator faults are, respectively, defined, which can be computed via solving simple linear programming (LP) problems. Moreover, we propose three detectability conditions to guarantee the detection of multiple multiplicative actuator faults by using the invariant set-based method. Finally, we provide effective selection guidance for the detection of different multiple multiplicative actuator faults by systematically analysing the conservatism and characteristics of these three guaranteed detectability conditions. At the end of this paper, an electrical circuit example is used to illustrate the effectiveness of the proposed method.