{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T09:59:08Z","timestamp":1773827948868,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,22]],"date-time":"2021-02-22T00:00:00Z","timestamp":1613952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Romanian Ministry of Research and Innovation","award":["project PN-IIIP2-2.1-PED-2019-0085 CONTRACT 447PED\/2020 (Acronim POSEIDON)."],"award-info":[{"award-number":["project PN-IIIP2-2.1-PED-2019-0085 CONTRACT 447PED\/2020 (Acronim POSEIDON)."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.<\/jats:p>","DOI":"10.3390\/sym13020353","type":"journal-article","created":{"date-parts":[[2021,2,22]],"date-time":"2021-02-22T20:42:51Z","timestamp":1614026571000},"page":"353","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sliding Mode Control and Geometrization Conjecture in Seismic Response"],"prefix":"10.3390","volume":"13","author":[{"given":"Ligia","family":"Munteanu","sequence":"first","affiliation":[{"name":"Institute of Solid Mechanics, Romanian Academy, Bucure\u0219ti 010141, Romania"}]},{"given":"Dan","family":"Dumitriu","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Romanian Academy, Bucure\u0219ti 010141, Romania"}]},{"given":"Cornel","family":"Brisan","sequence":"additional","affiliation":[{"name":"Department of Mechatronics and Machine Dynamics, Technical University from Cluj-Napoca, Cluj-Napoca 400114, Romania"}]},{"given":"Mircea","family":"Bara","sequence":"additional","affiliation":[{"name":"Department of Mechatronics and Machine Dynamics, Technical University from Cluj-Napoca, Cluj-Napoca 400114, Romania"}]},{"given":"Veturia","family":"Chiroiu","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Romanian Academy, Bucure\u0219ti 010141, Romania"}]},{"given":"Nicoleta","family":"Nedelcu","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Romanian Academy, Bucure\u0219ti 010141, Romania"}]},{"given":"Cristian","family":"Rugina","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Romanian Academy, Bucure\u0219ti 010141, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1002\/eqe.41","article-title":"Optimal control of linear buildings under seismic excitations","volume":"30","author":"Aldemir","year":"2001","journal-title":"Earthq. 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