{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/46634"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/46634","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Almost Lyapunov functions","abstract":"An autonomous, time-invariant dynamical system that verifies the classical Lyapunov criterion is globally asymptotically stable for the case when the Lyapunov function is strictly decreasing along the solution. We define an almost Lyapunov function to be a candidate Lyapunov function whose derivative with respect to time is of unknown sign in a set of small measure and negative elsewhere. We investigate the convergence of a system associated with an almost Lyapunov function. We show that for an unknown set of small enough measure, all the trajectories converge to a ball around the equilibrium point, under standard condition of Lipschitz continuity over the system and the derivative of the almost Lyapunov function.","abstract_html":"An autonomous, time-invariant dynamical system that verifies the classical Lyapunov criterion is globally asymptotically stable for the case when the Lyapunov function is strictly decreasing along the solution. We define an almost Lyapunov function to be a candidate Lyapunov function whose derivative with respect to time is of unknown sign in a set of small measure and negative elsewhere. We investigate the convergence of a system associated with an almost Lyapunov function. We show that for an unknown set of small enough measure, all the trajectories converge to a ball around the equilibrium point, under standard condition of Lipschitz continuity over the system and the derivative of the almost Lyapunov function.","abstract_has_math":false,"creators":["Ying, Charles"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Liberzon, Daniel M.","Zharnitsky, Vadim"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-16T17:56:55Z","date_published":"2014-01-16T17:56:55Z","updated_at":"2026-07-22T22:25:36Z","subjects":["Lyapunov stability","contraction","negativity of Lyapunov derivative","partial information"],"languages":["en"],"rights":["Copyright 2013 Charles Ying"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/46634","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Liberzon, Daniel M.","Zharnitsky, Vadim"]},{"key":"dc:creator","label":"Author","values":["Ying, Charles"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-01-16T17:56:55Z","2013-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Lyapunov stability","contraction","negativity of Lyapunov derivative","partial information"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 Charles Ying"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/46634"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["An autonomous, time-invariant dynamical system that verifies the classical Lyapunov criterion is globally asymptotically stable for the case when the Lyapunov function is strictly decreasing along the solution. We define an almost Lyapunov function to be a candidate Lyapunov function whose derivative with respect to time is of unknown sign in a set of small measure and negative elsewhere. We investigate the convergence of a system associated with an almost Lyapunov function. We show that for an unknown set of small enough measure, all the trajectories converge to a ball around the equilibrium point, under standard condition of Lipschitz continuity over the system and the derivative of the almost Lyapunov function.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-12-09T20:12:24Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 ecethesis.tex: 46656 bytes, checksum: 5e88addba7a08c40c48e83dfb3d230c3 (MD5) Ying_Charles.pdf: 461899 bytes, checksum: 2b5abe7f317a5a573db0f0be76af83ab (MD5)","Made available in DSpace on 2014-01-16T17:56:55Z (GMT). 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We show that for an unknown set of small enough measure, all the trajectories converge to a ball around the equilibrium point, under standard condition of Lipschitz continuity over the system and the derivative of the almost Lyapunov function.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-12-09T20:12:24Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 ecethesis.tex: 46656 bytes, checksum: 5e88addba7a08c40c48e83dfb3d230c3 (MD5) Ying_Charles.pdf: 461899 bytes, checksum: 2b5abe7f317a5a573db0f0be76af83ab (MD5)","Made available in DSpace on 2014-01-16T17:56:55Z (GMT). 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