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Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft.<\/jats:p>","DOI":"10.3390\/a14030088","type":"journal-article","created":{"date-parts":[[2021,3,14]],"date-time":"2021-03-14T22:13:10Z","timestamp":1615759990000},"page":"88","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1548-6547","authenticated-orcid":false,"given":"Andreas","family":"Rauh","sequence":"first","affiliation":[{"name":"ENSTA Bretagne, Lab-STICC, 29806 Brest, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0333-5872","authenticated-orcid":false,"given":"Auguste","family":"Bourgois","sequence":"additional","affiliation":[{"name":"ENSTA Bretagne, Lab-STICC, 29806 Brest, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0938-0615","authenticated-orcid":false,"given":"Luc","family":"Jaulin","sequence":"additional","affiliation":[{"name":"ENSTA Bretagne, Lab-STICC, 29806 Brest, France"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,14]]},"reference":[{"key":"ref_1","unstructured":"Kletting, M., Rauh, A., Aschemann, H., and Hofer, E.P. 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