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Linear residual generation for DAE systems has been considered. In all results derived, no distinction between input and output signals is done. A complete characterization and parameterization of all residual generators is presented. Further, a condition for fault detectability in DAE systems is given. Based on the characterization of all residual generators, a design strategy for residual generators for DAE systems is presented. Given that a set of faults are detectable, the design strategy will result in a residual generator sensitive to all the detectable faults. Further the residual generator is guaranteed to be of lowest possible order. Special care has been devoted to assure this property also for non-controllable systems.

A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the minimal polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding polynomial bases for null-spaces of polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the minimal polynomial basis approach can find all possible residual generators, including those of minimal McMillan degree, and the solution has a minimal parameterization. It is shown that some other well known design methods, do not have these properties.

Analyzing fault diagnosability performance for a given model, before developing a diagnosis algorithm, can be used to answer questions like "How difficult is it to detect a fault fi?" or "How difficult is it to isolate a fault fi from a fault fj?". The main contributions are the derivation of a measure, distinguishability, and a method for analyzing fault diagnosability performance of discrete-time descriptor models. The method, based on the Kullback-Leibler divergence, utilizes a stochastic characterization of the different fault modes to quantify diagnosability performance. Another contribution is the relation between distinguishability and the fault to noise ratio of residual generators. It is also shown how to design residual generators with maximum fault to noise ratio if the noise is assumed to be i.i.d. Gaussian signals. Finally, the method is applied to a heavy duty diesel engine model to exemplify how to analyze diagnosability performance of non-linear dynamic models.

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