Fault detection and isolation of Riesz spectral systems: A geometric approach

The Riesz spectral (RS) systems represent a large class of parabolic and hyperbolic partial differential equations (PDE) in infinite-dimensional systems. In this work, a fault detection and isolation (FDI) methodology for real diagonalizable RS systems is investigated by using a geometric approach. This paper is mainly concerned with the equivalency of different types of invariant subspaces defined for the RS systems and the necessary and sufficient conditions for solvability of the FDI problem. Moreover, for a subclass of RS systems, we first provide algorithms (for computing the invariant subspaces) that converge in a finite and known number of steps and then derive the necessary and sufficient conditions for solvability of the FDI problem.