7. Computational Issues

This chapter discusses the main computational issues underlying the synthesis procedures of fault detection filters presented in Chap. 5. The synthesis procedures of model detection filters, presented in Chap. 6, employ similar computational techniques, and, therefore, are entirely covered in this chapter. While all synthesis procedures have been developed in terms of input–output system representations, the underlying numerical algorithms exclusively rely on state-space representation-based computational methods. The discussion of the computational issues primarily focuses on exploiting all structural features present in the computational steps of the synthesis procedures and developing explicit updating formulas for the state-space representations of partial filter syntheses. All discussed computational procedures rely on the numerical algorithms described in details in Chap. 10, which fulfil standard quality requirements for satisfactory algorithms, such as generality, numerical reliability and computational efficiency.