Entirely left eigenstructure-assignment for fault diagnosis observers

In this paper a unified geometrically-embedded methodology of synthesis of static decoupled residual generators is presented that leads to a sub-optimal solution to a robust eigenstructure assignment problem based on a predetermined set of eigenvalues. Robustness of this design means that its eigenvector matrix is sufficiently well conditioned. An original idea of a convenient parameterisation of corresponding attainable eigensubspaces is developed and new conditions for disturbance decoupling are derived solely in terms of the left eigenvectors of a system observation state-transition matrix. The resolved completely-static disturbance-decoupling design problem can be treated as an effective preliminary-design stage of an integral synthesis of residual generators. A numerical example illustrates the effectiveness of the presented method.