Scaled Graph Bounding Techniques for Reset Systems
摘要
Reset systems can overcome fundamental limitations of linear time-invariant control. The recently introduced notion of scaled (relative) graphs provides a promising framework for developing graphical analysis and design tools for reset systems, in line with widely adopted loopshaping methods for linear systems. The aim of this paper is to derive techniques for over-bounding the scaled graph of reset systems, and obtain insights in their accuracy. We exploit connections between quadratic dissipativity and scaled graphs to recast the over-bounding problem as the search for piecewise quadratic storage functions. Using specific sampling techniques, we reveal a fundamental limitation of general scaled graph approximation methods that are based on quadratic dissipativity.
引用
@article{arxiv.2605.21119,
title = {Scaled Graph Bounding Techniques for Reset Systems},
author = {Timo de Groot and Maurice Heemels and Tom Oomen and Sebastiaan van den Eijnden},
journal= {arXiv preprint arXiv:2605.21119},
year = {2026}
}
备注
6 pages, 5 figures, To appear in 23rd IFAC World Congress Busan South Korea 2026