Error quantification of the normalised right graph symbol for an errors-in-variables system

This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol (NRGS) for an errors-in-variables (EIV) system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from textit{a priori} and textit{a posteriori} information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and ${rm H}_infty$-norm of their NRGSs' difference. The obtained NRGS perturbation model set paves the way for robust controller design using an ${rm H}_infty$ loop-shaping method because it is a standard form of the well-known NCF (normalized coprime factor) perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.