{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T14:48:57Z","timestamp":1772722137031,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T00:00:00Z","timestamp":1603670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software.<\/jats:p>","DOI":"10.3390\/sym12111771","type":"journal-article","created":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T10:38:35Z","timestamp":1603708715000},"page":"1771","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar Danilo","family":"Montoya","sequence":"first","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogot\u00e1 11021, Colombia"},{"name":"Laboratorio Inteligente de Energ\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, km 1 v\u00eda Turbaco, Cartagena 131001, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7609-1197","authenticated-orcid":false,"given":"Walter","family":"Gil-Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Grupo GIIEN, Facultad de Ingenier\u00eda, Instituci\u00f3n Universitaria Pascual Bravo, Campus Robledo, Medell\u00edn 050036, Colombia"},{"name":"Facultad de Ingenier\u00edas, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4189-9054","authenticated-orcid":false,"given":"Juan A.","family":"Dominguez-Jimenez","sequence":"additional","affiliation":[{"name":"Hydrogen Research Institute, Universit\u00e9 du Quebec \u00e0 Trois-Rivieres, Trois-Rivi\u00e8res, QC 3351, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2448-2174","authenticated-orcid":false,"given":"Alexander","family":"Molina-Cabrera","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00edas, Universidad Tecnol\u00f3gica de Pereira, Pereira 660003, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9983-4555","authenticated-orcid":false,"given":"Diego A.","family":"Giral-Ram\u00edrez","sequence":"additional","affiliation":[{"name":"Facultad Tecnol\u00f3gica, Universidad Distrital Francisco Jos\u00e9 de Caldas, Carrera 7 No. 40B-53, Bogot\u00e1 11021, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,26]]},"reference":[{"key":"ref_1","unstructured":"Isidori, A. 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