New computational paradigms in solving fault detection and isolation problems

A representative set of fault detection and isolation problems are formulated for linear time-invariant systems with additive faults. For all problems general existence conditions of their solutions are given. An overview of recently developed computational methods for the synthesis of fault detection filters is presented for all formulated problems. Two remarkable computational paradigms emerged in these developments, which are instrumental in developing generally applicable, numerically reliable and computationally efficient synthesis methods. The first paradigm is the use of integrated synthesis algorithms, where the resulting fault detection filters are determined by successive updating of partial syntheses addressing specific requirements. The second paradigm is the use of the nullspace method as a first synthesis step to reduce all synthesis problems to a simple standard form which allows to easily check solvability conditions and address least order synthesis problems.