{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69241"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69241","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Nonexplicit Singular Perturbations and Interconnected Systems","abstract":"Singular perturbations have been shown to be an effective tool in the analysis and design of systems with "slow" and "fast" dynamics. However, the use of this tool is often inhibited by the fact that when physical quantities are selected as state variables the model fails to be in the standard singularly perturbed form. In this thesis we deal with such nonexplicit models and show that for a wide class of problems a proper selection of variables leads to explicit singularly perturbed models. Equilibrium and conservation properties are shown to provide a coordinate-free characterization of two-time-scale systems. They also suggest a coordinate transformation that transforms nonexplicit models into explicit ones. This transformation is then used to study nonlinear high gain feedback systems, thus extending earlier linear results. It is also utilized to establish the relation between weak connections and time scales in interconnected systems whose subsystems possess a continuum of equilibrium points. Finally, the methodology is applied to reduced order modeling of dynamic networks and it is shown that linear conservation laws lead to a linear transformation separating the time scales even when some of the components of the network are nonlinear. Moreover, the reduced order model retains the physical meaning of the original system.","abstract_html":"Singular perturbations have been shown to be an effective tool in the analysis and design of systems with "slow" and "fast" dynamics. However, the use of this tool is often inhibited by the fact that when physical quantities are selected as state variables the model fails to be in the standard singularly perturbed form. In this thesis we deal with such nonexplicit models and show that for a wide class of problems a proper selection of variables leads to explicit singularly perturbed models. Equilibrium and conservation properties are shown to provide a coordinate-free characterization of two-time-scale systems. They also suggest a coordinate transformation that transforms nonexplicit models into explicit ones. This transformation is then used to study nonlinear high gain feedback systems, thus extending earlier linear results. It is also utilized to establish the relation between weak connections and time scales in interconnected systems whose subsystems possess a continuum of equilibrium points. Finally, the methodology is applied to reduced order modeling of dynamic networks and it is shown that linear conservation laws lead to a linear transformation separating the time scales even when some of the components of the network are nonlinear. Moreover, the reduced order model retains the physical meaning of the original system.","abstract_has_math":false,"creators":["Peponides, George Michael"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:04:23Z","date_published":"2014-12-15T19:04:23Z","updated_at":"2026-07-22T22:26:00Z","subjects":["Engineering, Electronics and Electrical"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8302959"],"render_values":[{"text":"(UMI)AAI8302959","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69241","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Peponides, George Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:04:23Z","10000-01-01","1982"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical 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, Electronics and Electrical"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69241","(UMI)AAI8302959"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Singular perturbations have been shown to be an effective tool in the analysis and design of systems with "slow" and "fast" dynamics. However, the use of this tool is often inhibited by the fact that when physical quantities are selected as state variables the model fails to be in the standard singularly perturbed form. In this thesis we deal with such nonexplicit models and show that for a wide class of problems a proper selection of variables leads to explicit singularly perturbed models. Equilibrium and conservation properties are shown to provide a coordinate-free characterization of two-time-scale systems. They also suggest a coordinate transformation that transforms nonexplicit models into explicit ones. This transformation is then used to study nonlinear high gain feedback systems, thus extending earlier linear results. It is also utilized to establish the relation between weak connections and time scales in interconnected systems whose subsystems possess a continuum of equilibrium points. Finally, the methodology is applied to reduced order modeling of dynamic networks and it is shown that linear conservation laws lead to a linear transformation separating the time scales even when some of the components of the network are nonlinear. Moreover, the reduced order model retains the physical meaning of the original system.","Made available in DSpace on 2014-12-15T19:04:23Z (GMT). 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However, the use of this tool is often inhibited by the fact that when physical quantities are selected as state variables the model fails to be in the standard singularly perturbed form. In this thesis we deal with such nonexplicit models and show that for a wide class of problems a proper selection of variables leads to explicit singularly perturbed models. Equilibrium and conservation properties are shown to provide a coordinate-free characterization of two-time-scale systems. They also suggest a coordinate transformation that transforms nonexplicit models into explicit ones. This transformation is then used to study nonlinear high gain feedback systems, thus extending earlier linear results. It is also utilized to establish the relation between weak connections and time scales in interconnected systems whose subsystems possess a continuum of equilibrium points. Finally, the methodology is applied to reduced order modeling of dynamic networks and it is shown that linear conservation laws lead to a linear transformation separating the time scales even when some of the components of the network are nonlinear. Moreover, the reduced order model retains the physical meaning of the original system.","Made available in DSpace on 2014-12-15T19:04:23Z (GMT). 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