{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/83839"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/83839","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A Semidefinite Programming Approach for Control of Systems Along Trajectories","abstract":"The second approach amounts to parametrizing the system equations about the trajectory, resulting in a nonstationary linear parameter-varying (NLPV) model, and then constructing an NLPV synthesis. Synthesis conditions are derived for NLPV systems using an operator theoretic framework with the ℓ 2-induced norm as the performance measure. These conditions are given in terms of structured operator inequalities. In general, evaluating the validity of these conditions is an infinite dimensional convex optimization problem; however, if the initial system is eventually periodic, they reduce to a finite dimensional semidefinite programming problem. Also, we give systematic approaches for the model reduction of stable as well as stabilizable NLPV models, along with means for evaluating the error resulting from the reduction process.","abstract_html":"The second approach amounts to parametrizing the system equations about the trajectory, resulting in a nonstationary linear parameter-varying (NLPV) model, and then constructing an NLPV synthesis. Synthesis conditions are derived for NLPV systems using an operator theoretic framework with the ℓ 2-induced norm as the performance measure. These conditions are given in terms of structured operator inequalities. In general, evaluating the validity of these conditions is an infinite dimensional convex optimization problem; however, if the initial system is eventually periodic, they reduce to a finite dimensional semidefinite programming problem. Also, we give systematic approaches for the model reduction of stable as well as stabilizable NLPV models, along with means for evaluating the error resulting from the reduction process.","abstract_has_math":false,"creators":["Farhood, Mazen Habib"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Dullerud, Geir E."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T21:12:24Z","date_published":"2015-09-25T21:12:24Z","updated_at":"2026-07-22T22:26:22Z","subjects":["Engineering, Mechanical"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3202090"],"render_values":[{"text":"(MiAaPQ)AAI3202090","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/83839","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dullerud, Geir E."]},{"key":"dc:creator","label":"Author","values":["Farhood, Mazen Habib"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T21:12:24Z","10000-01-01","2005"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"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":["Engineering, Mechanical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/83839","(MiAaPQ)AAI3202090"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The second approach amounts to parametrizing the system equations about the trajectory, resulting in a nonstationary linear parameter-varying (NLPV) model, and then constructing an NLPV synthesis. Synthesis conditions are derived for NLPV systems using an operator theoretic framework with the ℓ 2-induced norm as the performance measure. These conditions are given in terms of structured operator inequalities. In general, evaluating the validity of these conditions is an infinite dimensional convex optimization problem; however, if the initial system is eventually periodic, they reduce to a finite dimensional semidefinite programming problem. Also, we give systematic approaches for the model reduction of stable as well as stabilizable NLPV models, along with means for evaluating the error resulting from the reduction process.","Made available in DSpace on 2015-09-25T21:12:24Z (GMT). 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Synthesis conditions are derived for NLPV systems using an operator theoretic framework with the ℓ 2-induced norm as the performance measure. These conditions are given in terms of structured operator inequalities. In general, evaluating the validity of these conditions is an infinite dimensional convex optimization problem; however, if the initial system is eventually periodic, they reduce to a finite dimensional semidefinite programming problem. Also, we give systematic approaches for the model reduction of stable as well as stabilizable NLPV models, along with means for evaluating the error resulting from the reduction process.","Made available in DSpace on 2015-09-25T21:12:24Z (GMT). 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