Thresholding in Set‐Membership Approaches to Fault Isolation Using the Minkowski Functional

ABSTRACT In the context of model‐based diagnosis of dynamical systems, this article introduces the Minkowski functional as a new analytical thresholding tool for a generic set‐membership approach to FDI. This tool formalizes the threshold computation problem as a function upper‐ and lower‐bounding problem, and provides non‐specific inequalities that can be applied to residual signals for real‐time system analysis. In particular, this article provides two new characterizations of the linear transformation of a smooth convex set based on its Minkowski functional. These results are then illustrated by computing several thresholds to residual signals.