5. Synthesis of Fault Detection and Isolation Filters

This chapter presents general synthesis procedures of fault detection filters, which solve the fault detection problems formulated in Chap. 3. Two computational paradigms are instrumental in developing generally applicable, numerically reliable and computationally efficient synthesis methods. The first paradigm is the use of factorization-based synthesis methods, which leads to the so-called integrated computational algorithms, with strongly coupled successive computational steps. The second paradigm is the use of the nullspace method as a first synthesis step to reduce all synthesis problems to simpler problems, which allow to easily check the solvability conditions and address least-order synthesis problems. The synthesis procedures are described in terms of input–output models, which allow simpler conceptual presentations. The numerical aspects of equivalent state-space representation based synthesis algorithms are discussed in Chap. 7.