Fault detection and isolation of Fornasini-Marchesini 2D systems: A geometric approach

The fault detection and isolation (FDI) problem for discrete-time two-dimensional (2D) systems represented by the Fornasini-Marchesini model II is investigated in this work. It is shown that the sufficient conditions for solvability of the FDI problem that we have developed recently for the Roesser model is also applicable to this class of 2D systems. In this paper, we are mainly concerned with the necessary conditions. Two sets of necessary conditions for the solvability of the FDI problem are derived. The first necessary condition involves a new set of invariant subspaces that has no one-dimensional (1D) equivalency. The second set which is consistent with its equivalent 1D case is derived, generically (from the algebraic geometry point of view). A numerical example is also provided to illustrate the application of the results.