Test limitations induced by fault-driven instability of analog circuits

II. Methodology A. Modelling of faulty circuit with the aid of linear fractional transformation As the first step of stability analysis, the model of CUT with faults in its physical parameters must be designed on a unified linear fractional transformation (LFT) framework [12]. Suppose G(s) is a stable, real rational transfer function matrix of a linear time invariant CUT. The idea is to separate what is known from what is unknown in a feedback-like structure. Fault may be modelled as unknown perturbations to the known nominal model. The CUT can be put in the general diagram in Fig.1, where G is the transfer matrix, ∆ is the representation of parametric faults (matrix of perturbations of transfer function coefficients caused by parametric faults). The signals u, y, w and z are vector quantities. The matrix G can be partitioned into four submatrices compatible with the sizes of the signal vectors.