ABSTRACT
This chapter starts with the recollection of the mechanism and conditions of perfect decoupling, as applied to additive disturbances and parametric uncertainties, combined with various fault isolation strategies. It achieves optimal robustness by searching over a discrete set of possible parity relations, rather than by adjusting residual generator parameters. The chapter presents an approximate decoupling approach. It achieves optimal approximate disturbance decoupling, combined with structured or directional fault isolation, via the minimization of a quadratic performance index under linear equality constraints. The chapter outlines the main ideas of residual generator design by the H8 methodology, as applied to additive faults and disturbances. Approximate decoupling by rank reduced approximation provides significant flexibility, allowing for the implementation of a variety of fault isolation strategies. The singular value decomposition technique is the extension, to general rectangular matrices, of the spectral decomposition procedure of square matrices.
