Frequency domain identifiability and sloppiness of descriptor systems with an LFT structure

Abstract

Identifiability and sloppiness are investigated in this paper for the parameters of a descriptor system based on its frequency responses. Two metrics are suggested respectively for measuring absolute and relative sloppiness of the parameter vector. In this descriptor system, system matrices are assumed to depend on its parameters through a linear fractional transformation, which enables it to include a large class of networked dynamic systems as a special case. When an associated transfer function matrix is of full normal row rank, a matrix rank based necessary and sufficient condition is derived for parameter identifiability. This condition can be verified recursively. An algorithm is suggested to find a set of frequencies, at which system frequency responses are capable to uniquely determine its parameter values. An ellipsoid approximation is given for the set consisting of all the parameter values of the descriptor system, whose frequency response deviates within a prescribed distance from that associated with a globally identifiable parameter vector value. Explicit formulas are also derived for the suggested absolute and relative sloppiness metrics for some application significant cases.