Certifying Set Attractivity for Discrete-Time Uncertain Nonlinear Switched Systems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918534153502720 |
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| author | Anderson, Alejandro Hernandez-Vargas, Esteban A. Giordano, Giulia |
| author_facet | Anderson, Alejandro Hernandez-Vargas, Esteban A. Giordano, Giulia |
| contents | We introduce a new class of functions, called Attractivity Guarantee (AG)-functions, to certify the attractivity of sets for uncertain nonlinear switched systems in discrete time. The existence of an AG-function associated with a set guarantees the robust local attractivity of that set under the system dynamics. We propose a constructive method for obtaining piecewise-continuous AG-functions based on contractive sets for the system, and show that the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function, and hence the robust local attractivity of the set itself. We illustrate the proposed framework through examples that elucidate the theoretical concepts, and through the case study of a nonlinear switched system modelling antimicrobial resistance, which highlights the practical relevance of the approach to the analysis of biological systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Certifying Set Attractivity for Discrete-Time Uncertain Nonlinear Switched Systems Anderson, Alejandro Hernandez-Vargas, Esteban A. Giordano, Giulia Systems and Control We introduce a new class of functions, called Attractivity Guarantee (AG)-functions, to certify the attractivity of sets for uncertain nonlinear switched systems in discrete time. The existence of an AG-function associated with a set guarantees the robust local attractivity of that set under the system dynamics. We propose a constructive method for obtaining piecewise-continuous AG-functions based on contractive sets for the system, and show that the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function, and hence the robust local attractivity of the set itself. We illustrate the proposed framework through examples that elucidate the theoretical concepts, and through the case study of a nonlinear switched system modelling antimicrobial resistance, which highlights the practical relevance of the approach to the analysis of biological systems. |
| title | Certifying Set Attractivity for Discrete-Time Uncertain Nonlinear Switched Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2511.13906 |