Sloppiness of Structured Systems with a Matrix Fraction Description

This paper attacks practical difficulties in estimating parameters of a matrix fraction described system. Results on the sloppiness of a linear functional transformation (LFT) described descriptor system have been extended. Besides the assumptions that both the numerator and denominator polynomial matrices depend affinely on system parameters, and the denominator polynomial matrix is invertible, not any other hypothesis is adopted. An ellipsoid approximation is obtained for the parameter set constituted from all the parameter values, with the associated system frequency responses deviating within a specified range from those of the system with a known parameter value. For some significant application cases, explicit expressions were derived for the absolute and relative slop-piness. Comparisons with the well-known Fisher information matrix have also been performed through a mechanical system, revealing significant differences between them in quantifying parameter estimation hardness.