Set-membership state observers design based on explicit characterizations of theestimation-error bounds

Abstract : In This work, we propose two main new approaches for the set-membershipstate estimation problem based on explicit characterization of the estimation error bounds. These approaches can be seen as a combination between a punctual observer and a setmembership characterization of the observation error. The objective is to reduce the complexity of the on-line implimentation, reduce the on-line computation time and improve the accuracy of the estimated state enclosure.The first approach is a set-membership observer based on ellipsoidal invariant sets for linear discrete-time systems and also for Linear Parameter Varying systems. The proposed approach provides a deterministic state interval that is build as the sum of the estimated system states and its corresponding estimation error bounds. The important feature of the proposed approach is that does not require propagation of sets.The second approach is an interval version of the Luenberger state observer for uncertain discrete-time linear systems based on interval and invariant set computation. The setmembership state estimation problem is considered as a punctual state estimation issue coupled with an interval characterization of the estimation error.
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Nassim Loukkas. Set-membership state observers design based on explicit characterizations of theestimation-error bounds. Automatic. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAT040⟩. ⟨tel-01898259⟩

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