Multiple Multiplicative Actuator Fault Detectability Analysis Based on Invariant Sets for Discrete-time LPV Systems

Abstract

This paper proposes a generalized minimum detectable fault (MDF) computation method based on the set-separation condition between the healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded inputs and uncertainties. First, we equivalently transform the multiple multiplicative actuator faults into the form of multiple additive actuator faults, which is beneficial to simplify the problem. Then, by considering the 1-norm of the fault vector, we define the generalized MDF in the case of multiple additive actuator faults, which can be computed via solving a simple linear programming (LP) problem. Moreover, an analysis of the effect of the input vector on the magnitude of the generalized MDF is made. Since the proposed generalized MDF computation method is robust by considering the bounds of inputs and uncertainties, robust fault detection (FD) can be guaranteed whenever the sum of the magnitudes of all occurred faults is larger than the magnitude of the generalized MDF. At the end of this paper, a numerical example is used to illustrate the effectiveness of the proposed method.