Using Seminorms To Analyze Contraction of Switched Systems With Only Non-Contracting Modes
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908719980216320 |
|---|---|
| author | Baum, Edwin Liu, Zonglin Qin, Yuzhen Stursberg, Olaf |
| author_facet | Baum, Edwin Liu, Zonglin Qin, Yuzhen Stursberg, Olaf |
| contents | This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that unstable systems may still exhibit stable behavior within certain subspaces, conditions are provided which ensure contracting evolution within a given subspace of the state space of the switched system. These conditions are derived using the concepts of seminorms and semi-contracting systems. Then, by selecting a set of subspaces whose corresponding seminorms form a separating family of the state space, and by verifying whether a given mode is contracting in each subspace, conditions on the activation time of each mode are provided by which contraction on the complete state space is guaranteed. Numerical examples are presented for illustration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Using Seminorms To Analyze Contraction of Switched Systems With Only Non-Contracting Modes Baum, Edwin Liu, Zonglin Qin, Yuzhen Stursberg, Olaf Systems and Control This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that unstable systems may still exhibit stable behavior within certain subspaces, conditions are provided which ensure contracting evolution within a given subspace of the state space of the switched system. These conditions are derived using the concepts of seminorms and semi-contracting systems. Then, by selecting a set of subspaces whose corresponding seminorms form a separating family of the state space, and by verifying whether a given mode is contracting in each subspace, conditions on the activation time of each mode are provided by which contraction on the complete state space is guaranteed. Numerical examples are presented for illustration. |
| title | Using Seminorms To Analyze Contraction of Switched Systems With Only Non-Contracting Modes |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.16338 |