A networked small-gain theorem based on discrete-time diagonal stability
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913572572889088 |
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| author | Ofir, Ron Margaliot, Michael |
| author_facet | Ofir, Ron Margaliot, Michael |
| contents | We present a new sufficient condition for finite-gain $L_2$ input-to-output stability of a networked system. The condition requires a matrix, that combines information on the $L_2$ gains of the sub-systems and their interconnections, to be discrete-time diagonally stable (DTDS). We show that the new result generalizes the standard small gain theorem for the negative feedback connection of two sub-systems. An important advantage of the new result is that known sufficient conditions for DTDS can be applied to derive sufficient conditions for networked input-to-output stability. We demonstrate this using several examples. We also derive a new necessary and sufficient condition for a matrix that is a rank one perturbation of a Schur diagonal matrix to be DTDS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A networked small-gain theorem based on discrete-time diagonal stability Ofir, Ron Margaliot, Michael Systems and Control Optimization and Control We present a new sufficient condition for finite-gain $L_2$ input-to-output stability of a networked system. The condition requires a matrix, that combines information on the $L_2$ gains of the sub-systems and their interconnections, to be discrete-time diagonally stable (DTDS). We show that the new result generalizes the standard small gain theorem for the negative feedback connection of two sub-systems. An important advantage of the new result is that known sufficient conditions for DTDS can be applied to derive sufficient conditions for networked input-to-output stability. We demonstrate this using several examples. We also derive a new necessary and sufficient condition for a matrix that is a rank one perturbation of a Schur diagonal matrix to be DTDS. |
| title | A networked small-gain theorem based on discrete-time diagonal stability |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2411.03380 |