  This paper deals with the fault detection and isolation (FDI) problem for
linear structured systems in which the system matrices are given by
zero/nonzero/arbitrary pattern matrices. In this paper, we follow a geometric
approach to verify solvability of the FDI problem for such systems. To do so,
we first develop a necessary and sufficient condition under which the FDI
problem for a given particular linear time-invariant system is solvable. Next,
we establish a necessary condition for solvability of the FDI problem for
linear structured systems. In addition, we develop a sufficient algebraic
condition for solvability of the FDI problem in terms of a rank test on an
associated pattern matrix. To illustrate that this condition is not necessary,
we provide a counterexample in which the FDI problem is solvable while the
condition is not satisfied. Finally, we develop a graph-theoretic condition for
the full rank property of a given pattern matrix, which leads to a
graph-theoretic condition for solvability of the FDI problem.
