Gap Metric Bound Construction From Frequency Response Data

Abstract

Motivated by the difficulty of designing low-order controllers for large-scale plants consisting of numerous interconnected subsystems, this paper addresses the issue of quantifying the ν-gap metric between the plant and a lower-order identified model, using only plant frequency response data. The main result of this paper is the construction of a bound on the ν-gap metric between plant and model that exploits the convergence properties of Chebyshev polynomial interpolants of point-wise in frequency system graph symbols. This bound subsequently informs the design of low-order robust controllers synthesised from the identified model. The techniques developed in this paper are demonstrated upon a semi-discretised 1D heat equation.