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The homological perturbation lemma and its applications to robust stabilization

Alban Quadrat 1
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
Abstract : Within the lattice approach to analysis and synthesis problems, we show how standard results on robust stabilization can be obtained in a unified way and generalized when interpreted as a particular case of the so-called homological perturbation lemma. This lemma plays a significant role in algebraic topology, homological algebra, computer algebra, etc. Our results show that it is also central to robust control theory for (infinite-dimensional) linear systems.
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Submitted on : Thursday, January 21, 2016 - 12:37:44 PM
Last modification on : Wednesday, September 16, 2020 - 5:25:47 PM

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Alban Quadrat. The homological perturbation lemma and its applications to robust stabilization. 8th IFAC Symposium on Robust Control Design (ROCOND), Jul 2015, Bratislava, Slovakia. ⟨10.1016/j.ifacol.2015.09.425⟩. ⟨hal-01259960⟩

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