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Homogeneous Observers for Projected Quadratic Partial Differential Equations

Sergiy Zhuk 1 Andrey Polyakov 2
2 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 a new homogeneous observer for finite-dimensional projections of quadratic homogeneous hyperbolic PDEs with compact state space. The design relies upon new sufficient conditions for fixed-time convergence of observer's gain, described as a solution of a non-linear homogeneous matrix differential equations, towards an ellipsoid in the space of symmetric non-negative matrices. Convergence of the observer is analyzed, and a numerical convergence test is proposed: numerical experiments confirm the test on ODEs obtained by finite-difference discretization of Burgers-Hopf equation.
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Contributor : Andrey Polyakov <>
Submitted on : Wednesday, July 22, 2020 - 11:20:19 AM
Last modification on : Friday, December 11, 2020 - 6:44:08 PM
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  • HAL Id : hal-02904474, version 1



Sergiy Zhuk, Andrey Polyakov. Homogeneous Observers for Projected Quadratic Partial Differential Equations. IEEE Conference on Decision and Control, Dec 2020, Jesu Island, South Korea. ⟨hal-02904474⟩



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