Passivity theorems for input-to-state stability of forced Lur'e inclusions and equations, and consequent entrainment-type properties
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916296454569984 |
|---|---|
| author | Guiver, Chris |
| author_facet | Guiver, Chris |
| contents | A suite of input-to-state stability results are presented for a class of forced differential inclusions, so-called Lur'e inclusions. As a consequence, semi-global incremental input-to-state stability results for systems of forced Lur'e differential equations are derived. The results are in the spirit of the passivity theorem from control theory as both the linear and nonlinear components of the Lur'e inclusion (or equation) are assumed to satisfy passivity-type conditions. These results provide a basis for the analysis of forced Lur'e differential equations subject to (almost) periodic forcing terms and, roughly speaking, ensure the existence and attractivity of (almost) periodic state- and output-responses, comprising another focus of the present work. One ultimate aim of the study is to provide a robust and rigorous theoretical foundation for a well-defined and tractable ``frequency response'' of forced Lur'e systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Passivity theorems for input-to-state stability of forced Lur'e inclusions and equations, and consequent entrainment-type properties Guiver, Chris Optimization and Control Systems and Control Classical Analysis and ODEs 34A12, 34A60, 34C27, 34D20, 93C10, 93C35, 93D09, 93D15 A suite of input-to-state stability results are presented for a class of forced differential inclusions, so-called Lur'e inclusions. As a consequence, semi-global incremental input-to-state stability results for systems of forced Lur'e differential equations are derived. The results are in the spirit of the passivity theorem from control theory as both the linear and nonlinear components of the Lur'e inclusion (or equation) are assumed to satisfy passivity-type conditions. These results provide a basis for the analysis of forced Lur'e differential equations subject to (almost) periodic forcing terms and, roughly speaking, ensure the existence and attractivity of (almost) periodic state- and output-responses, comprising another focus of the present work. One ultimate aim of the study is to provide a robust and rigorous theoretical foundation for a well-defined and tractable ``frequency response'' of forced Lur'e systems. |
| title | Passivity theorems for input-to-state stability of forced Lur'e inclusions and equations, and consequent entrainment-type properties |
| topic | Optimization and Control Systems and Control Classical Analysis and ODEs 34A12, 34A60, 34C27, 34D20, 93C10, 93C35, 93D09, 93D15 |
| url | https://arxiv.org/abs/2406.15099 |