On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916056323325952 |
|---|---|
| author | Niu, Zirui Astolfi, Daniele Scarciotti, Giordano |
| author_facet | Niu, Zirui Astolfi, Daniele Scarciotti, Giordano |
| contents | Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28665 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation Niu, Zirui Astolfi, Daniele Scarciotti, Giordano Systems and Control Optimization and Control Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations. |
| title | On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2605.28665 |