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On Galerkin Method for Homogeneous Infinite-Dimensional Systems

Andrey Polyakov 1
1 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : The paper proposes Galerkin-like projection method which preserves dilation symmetries of linear and nonlinear (possibly unbounded) operators. The method is developed for approximation of generalized homogeneous evolution equations in Hilbert spaces. It is shown that the obtained reduced-order model preserve stability and convergence properties (such as finite-time and fixed-time stability) of the original system. The proposed method is compared on simulations with the classical Galerkin method for the Burgers equation. Key word. approximation of distributed parameter systems; semigroup and operator theory.
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https://hal.inria.fr/hal-02926265
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Submitted on : Monday, August 31, 2020 - 3:25:56 PM
Last modification on : Friday, January 22, 2021 - 3:30:47 AM
Long-term archiving on: : Tuesday, December 1, 2020 - 12:40:27 PM

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Andrey Polyakov. On Galerkin Method for Homogeneous Infinite-Dimensional Systems. 2020. ⟨hal-02926265⟩

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