Super-twisting over networks: A Lyapunov approach for distributed differentiation
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914301099376640 |
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| author | Aldana-López, Rodrigo Salesa, Irene Perez Gutierrez, David Gomez Aragues, Rosario Sagues, Carlos |
| author_facet | Aldana-López, Rodrigo Salesa, Irene Perez Gutierrez, David Gomez Aragues, Rosario Sagues, Carlos |
| contents | We study distributed differentiation, where agents in a networked system estimate the average of local time-varying signals and their derivatives under mild assumptions on the agents' signals and their first and second derivatives. Existing sliding-mode methods provide only local stability guarantees and lack systematic gain selection. By isolating the structural features shared with the super-twisting algorithm and encoding them into an abstract model, we construct a Lyapunov function enabling systematic gain design and proving global finite-time convergence to consensus for the distributed differentiator. Building on this framework, we develop an event-triggered hybrid system implementation using time-varying and state dependent threshold rules and derive minimum inter-event time guarantees and accuracy bounds that quantify the trade-off between estimation accuracy and communication effort. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01857 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Super-twisting over networks: A Lyapunov approach for distributed differentiation Aldana-López, Rodrigo Salesa, Irene Perez Gutierrez, David Gomez Aragues, Rosario Sagues, Carlos Systems and Control Optimization and Control We study distributed differentiation, where agents in a networked system estimate the average of local time-varying signals and their derivatives under mild assumptions on the agents' signals and their first and second derivatives. Existing sliding-mode methods provide only local stability guarantees and lack systematic gain selection. By isolating the structural features shared with the super-twisting algorithm and encoding them into an abstract model, we construct a Lyapunov function enabling systematic gain design and proving global finite-time convergence to consensus for the distributed differentiator. Building on this framework, we develop an event-triggered hybrid system implementation using time-varying and state dependent threshold rules and derive minimum inter-event time guarantees and accuracy bounds that quantify the trade-off between estimation accuracy and communication effort. |
| title | Super-twisting over networks: A Lyapunov approach for distributed differentiation |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2602.01857 |