Robust LPV Modeling of Precision Motion Systems Via Edge-Theorem Verification

Abstract

This work proposes a systematic workflow for constructing grid-based Linear Parameter-Varying (LPV) models from frequency response data. Transfer functions are estimated at multiple scheduling-parameter grid points, fitted with a fixed model order, and transformed into controllable canonical realizations to ensure structural consistency. These vertex models are interpolated into an LPV state-space representation, while robust stability is verified using the Edge Theorem, which reduces the problem to checking edge polynomials of the convex hull. The novelty of the approach lies in integrating frequency-domain identification, canonical-form embedding, and polytope-based robust stability analysis into a unified LPV framework. Unlike conventional methods that rely on time-domain experiments or subspace techniques, the proposed method exploits experimentally accessible frequency-response data and avoids coordinate mismatches during interpolation. Validation on a precision motion system demonstrates both theoretical soundness and practical applicability, confirming the workflow as a reliable pathway from frequency-domain data to robust LPV control design.