Identification of higher-dimensional ill-conditioned systems using extensions of virtual transfer function between inputs

A new formulation is proposed to directly extend the virtual transfer function between inputs (VTFBI) approach to ill-conditioned systems with dimensions higher than 2 × 2. The method requires only a single correlated component and is applicable to moderately large systems of up to around six outputs. To cater for systems with even higher dimensions, an indirect approach is further introduced based on subsystem decomposition in which the design for each subsystem achieves D-optimality in the presence of active output variance constraints. New measures of sensitivity to measurement inaccuracy and parameter changes are also introduced. A detailed case study shows that both direct and indirect extensions of the VTFBI technique outperform competing ones in terms of accuracy in the estimation of singular values, robustness towards the effect of noise as well as effectiveness for application in model based control. An additional advantage of the proposed approaches is that their performance does not depend significantly on the specific design choices made within these methods.