{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/95430"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/95430","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Topological entropy bounds for switched linear systems with lie structure","abstract":"In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time horizons, in the limit. After working out entropy computations in detail for the scalar switched case, we review the linear time-invariant nonscalar case, and extend to the nonscalar switched case. We assume some commutation relations among the matrices of the switched system, namely solvability, define an “upper average time of activation” quantity and use it to provide an upper bound on the entropy of the switched system in terms of the eigenvalues of each subsystem.","abstract_html":"In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time horizons, in the limit. After working out entropy computations in detail for the scalar switched case, we review the linear time-invariant nonscalar case, and extend to the nonscalar switched case. We assume some commutation relations among the matrices of the switched system, namely solvability, define an “upper average time of activation” quantity and use it to provide an upper bound on the entropy of the switched system in terms of the eigenvalues of each subsystem.","abstract_has_math":false,"creators":["Schmidt, A. James"],"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":["Belabbas, Mohamed A.","Liberzon, Daniel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-03-01T15:51:12Z","date_published":"2017-03-01T15:51:12Z","updated_at":"2026-07-22T22:26:37Z","subjects":["Switched Systems","Topological Entropy"],"languages":["en"],"rights":["2016 by A. James Schmidt"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/95430","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Belabbas, Mohamed A.","Liberzon, Daniel"]},{"key":"dc:creator","label":"Author","values":["Schmidt, A. James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-03-01T15:51:12Z","2016-10-14","2016-12"]},{"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":["Switched Systems","Topological Entropy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["2016 by A. James Schmidt"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/95430"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time horizons, in the limit. After working out entropy computations in detail for the scalar switched case, we review the linear time-invariant nonscalar case, and extend to the nonscalar switched case. We assume some commutation relations among the matrices of the switched system, namely solvability, define an “upper average time of activation” quantity and use it to provide an upper bound on the entropy of the switched system in terms of the eigenvalues of each subsystem.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-02-28 without embargo terms","The student, A. Schmidt, accepted the attached license on 2016-10-07 at 17:31.","The student, A. Schmidt, submitted this Thesis for approval on 2016-10-07 at 17:35.","This Thesis was approved for publication on 2016-10-14 at 11:18.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9059 on 2017-02-28 at 14:44:44","Made available in DSpace on 2017-03-01T15:51:12Z (GMT). No. of bitstreams: 2 SCHMIDT-THESIS-2016.pdf: 256253 bytes, checksum: bf90c8e6fd7f9932ae694436072d5231 (MD5) LICENSE.txt: 4210 bytes, checksum: b465b39bcaf2aa43ce12c062deca7145 (MD5) Previous issue date: 2016-10-14"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Topological entropy bounds for switched linear systems with lie structure"]}]}],"canonical_facts":{"dc:contributor":["Belabbas, Mohamed A.","Liberzon, Daniel"],"dc:creator":["Schmidt, A. James"],"dc:date":["2017-03-01T15:51:12Z","2016-10-14","2016-12"],"dc:description":["In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time horizons, in the limit. After working out entropy computations in detail for the scalar switched case, we review the linear time-invariant nonscalar case, and extend to the nonscalar switched case. We assume some commutation relations among the matrices of the switched system, namely solvability, define an “upper average time of activation” quantity and use it to provide an upper bound on the entropy of the switched system in terms of the eigenvalues of each subsystem.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-02-28 without embargo terms","The student, A. Schmidt, accepted the attached license on 2016-10-07 at 17:31.","The student, A. Schmidt, submitted this Thesis for approval on 2016-10-07 at 17:35.","This Thesis was approved for publication on 2016-10-14 at 11:18.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9059 on 2017-02-28 at 14:44:44","Made available in DSpace on 2017-03-01T15:51:12Z (GMT). No. of bitstreams: 2 SCHMIDT-THESIS-2016.pdf: 256253 bytes, checksum: bf90c8e6fd7f9932ae694436072d5231 (MD5) LICENSE.txt: 4210 bytes, checksum: b465b39bcaf2aa43ce12c062deca7145 (MD5) Previous issue date: 2016-10-14"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/95430"],"dc:language":["en"],"dc:rights":["2016 by A. James Schmidt"],"dc:subject":["Switched Systems","Topological Entropy"],"dc:title":["Topological entropy bounds for switched linear systems with lie structure"],"dc:type":["text"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:37Z"}