Generalized Lyapunov conditions for k-contraction: analysis and feedback design
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929522918555648 |
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| author | Cecilia, Andreu Zoboli, Samuele Astolfi, Daniele Serres, Ulysse Andrieu, Vincent |
| author_facet | Cecilia, Andreu Zoboli, Samuele Astolfi, Daniele Serres, Ulysse Andrieu, Vincent |
| contents | Recently, the concept of k-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of k-contraction properties has faced significant challenges due to the reliance on complex mathematical objects called matrix compounds. As a result, related control design methodologies have yet to appear in the literature. In this paper, we overcome existing limitations and propose new sufficient conditions for k-contraction which do not require matrix compounds computation. Notably, these conditions are also necessary in the linear time-invariant framework. Leveraging on these findings, we propose a feedback design methodology for both the linear and the nonlinear scenarios which can be used to enforce k-contractivity properties on the closed-loop dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_18388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Lyapunov conditions for k-contraction: analysis and feedback design Cecilia, Andreu Zoboli, Samuele Astolfi, Daniele Serres, Ulysse Andrieu, Vincent Systems and Control Dynamical Systems Recently, the concept of k-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of k-contraction properties has faced significant challenges due to the reliance on complex mathematical objects called matrix compounds. As a result, related control design methodologies have yet to appear in the literature. In this paper, we overcome existing limitations and propose new sufficient conditions for k-contraction which do not require matrix compounds computation. Notably, these conditions are also necessary in the linear time-invariant framework. Leveraging on these findings, we propose a feedback design methodology for both the linear and the nonlinear scenarios which can be used to enforce k-contractivity properties on the closed-loop dynamics. |
| title | Generalized Lyapunov conditions for k-contraction: analysis and feedback design |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2311.18388 |