Scaled Graph Bounding Techniques for Reset Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914583145349120 |
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| author | de Groot, Timo Heemels, Maurice Oomen, Tom Eijnden, Sebastiaan van den |
| author_facet | de Groot, Timo Heemels, Maurice Oomen, Tom Eijnden, Sebastiaan van den |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21119 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scaled Graph Bounding Techniques for Reset Systems de Groot, Timo Heemels, Maurice Oomen, Tom Eijnden, Sebastiaan van den Optimization and Control Systems and Control 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. |
| title | Scaled Graph Bounding Techniques for Reset Systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2605.21119 |