Integral Quadratic Constraints on Linear Infinite-dimensional Systems for Robust Stability Analysis
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866912935134101504 |
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| author | Barreau, Matthieu Scherer, Carsten W. Gouaisbaut, Frederic Seuret, Alexandre |
| author_facet | Barreau, Matthieu Scherer, Carsten W. Gouaisbaut, Frederic Seuret, Alexandre |
| contents | This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints (IQCs) and expressed in terms of two linear matrix inequalities with a moderate computational burden. The IQCs are not generated using dissipation inequalities involving the whole state of an infinite-dimensional system, but by using projection coefficients of the infinite-dimensional state. This permits to generalize our robustness result to many other PDEs. The proposed methodology is applied to a time-delay system and numerical results comparable to those in the literature are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_06283 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Integral Quadratic Constraints on Linear Infinite-dimensional Systems for Robust Stability Analysis Barreau, Matthieu Scherer, Carsten W. Gouaisbaut, Frederic Seuret, Alexandre Optimization and Control Analysis of PDEs This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints (IQCs) and expressed in terms of two linear matrix inequalities with a moderate computational burden. The IQCs are not generated using dissipation inequalities involving the whole state of an infinite-dimensional system, but by using projection coefficients of the infinite-dimensional state. This permits to generalize our robustness result to many other PDEs. The proposed methodology is applied to a time-delay system and numerical results comparable to those in the literature are obtained. |
| title | Integral Quadratic Constraints on Linear Infinite-dimensional Systems for Robust Stability Analysis |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2003.06283 |