Invariant-set based minimal detectable fault computation of discrete-time LPV systems with bounded uncertainties

Abstract

This paper proposes a minimal detectable fault (MDF) computation method based on the set-separation condition between the healthy and faulty residual sets for discretetime linear parameter varying (LPV) systems with bounded uncertainties. First, an invariant-set computation method for discrete-time LPV systems is developed exclusively based on a sequence of convex-set operations. Notably, this method goes beyond the existence condition of a common quadratic Lyapunov function for all the vertices of the parametric uncertainty. Based on asymptotic stability assumptions, a family of outerapproximations of minimal robust positively invariant (mRPI) set are obtained by using a shrinking procedure. Then, by considering the dual problem of the set-separation constraint regarding the healthy and faulty residual sets, we transform the guaranteed MDF problem based on the set-separation constraint into a simple linear programming problem to compute the magnitude of MDF. Since the proposed MDF computation method is robust regardless of the value of scheduling variables in a given convex set, fault detection (FD) can be guaranteed whenever the magnitude of fault is larger than that of the MDF. The detection method is shown to be effective for a microbial growth process.