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Pré-Publication, Document De Travail Année : 2023

Arbitrarily Fast Robust KKL Observer for Nonlinear Time-varying Discrete Systems

Gia Quoc Bao Tran
Pauline Bernard

Résumé

This work presents the Kazantzis-Kravaris/Luenberger (KKL) observer design for nonlinear time-varying discrete systems. We first give sufficient results on the existence of a sequence of functions T_k transforming the given system dynamics into an exponentially stable filter of the output in some other target coordinates, where an observer is directly designed. Then, we prove that under uniform Lipschitz backward distinguishability, the maps T_k become uniformly Lipschitz injective after a certain time, if the target dynamics is pushed sufficiently fast. This leads to an arbitrarily fast discrete observer, which exhibits similarities with the famous high-gain observer for continuous-time systems. Input-to-state stability of the estimation error with respect to uncertainties, input disturbances, and measurement noise is then shown. Next, under the milder backward distinguishability, we show the injectivity of the maps T_k after a certain time for a generic choice of the target filter dynamics. Examples including a discretized permanent magnet synchronous motor (PMSM) illustrate the proposed observer.
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Dates et versions

hal-03979381 , version 1 (08-02-2023)
hal-03979381 , version 2 (16-06-2023)
hal-03979381 , version 3 (26-10-2023)
hal-03979381 , version 4 (09-11-2023)

Identifiants

  • HAL Id : hal-03979381 , version 1

Citer

Gia Quoc Bao Tran, Pauline Bernard. Arbitrarily Fast Robust KKL Observer for Nonlinear Time-varying Discrete Systems. 2023. ⟨hal-03979381v1⟩
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