A geometric approach to fault detection and isolation of multi-dimensional (n-D) systems

Abstract

In this work, we develop a novel fault detection and isolation (FDI) scheme for discrete-time multi-dimensional (n-D) systems for the first time in the literature. These systems represent as generalization of the Fornasini-Marchesini model II two- and three-dimensional (2-D and 3-D) systems. This is accomplished by extending the geometric FDI approach of one-dimensional (1-D) systems to n-D systems. The basic invariant subspaces including unobservable, conditioned invariant and unobservability subspaces of 1-D systems are generalized to n-D models. These extensions have been achieved and facilitated by representing an n-D model as an infinite dimensional system, and by particularly constructing algorithms that compute these subspaces in a finite and known number of steps. By utilizing the introduced subspaces the FDI problem is formulated and necessary and sufficient conditions for its solvability are provided. Sufficient conditions for solvability of the FDI problem for n-D systems using LMI filters are also developed. Moreover, the capabilities and advantages of our proposed approach are demonstrated by performing an analytical comparison with the only currently available 3-D geometric methods in the literature. 1 2016, Springer Science+Business Media New York.