{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69258"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69258","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Analysis and Control of a Class of Stiff Linear Distributed Systems","abstract":"This thesis examines a class of systems whose models are described by linear partial differential equations that depend on a small parameter (epsilon). First, the spectral decomposition of the so-called "stiff" operators (using the terminology of {24}) is investigated, including the convergence of their eigenvalue-eigenvector pairs as (epsilon) (--->) 0, with the objective of clarifying their singular behavior. Second, asymptotic approximation of the solution boundary value problems involving stiff operators are constructed, using the weak limits of their eigenvectors. This approach leads to a decomposition into "regular" approximation and "internal layer" approximation, which are found separately and then combined to provide an approximation to the original problem. This methodology is not complicated. Moreover, it alleviates the inherent stiffness when numerical algorithms are employed. Third, the same approach is applied to some control problems. In this case, similar results are obtained, provided additional requirements are satisfied, due to the type of control, which may drastically alter the system behavior.","abstract_html":"This thesis examines a class of systems whose models are described by linear partial differential equations that depend on a small parameter (epsilon). First, the spectral decomposition of the so-called "stiff" operators (using the terminology of {24}) is investigated, including the convergence of their eigenvalue-eigenvector pairs as (epsilon) (--->) 0, with the objective of clarifying their singular behavior. Second, asymptotic approximation of the solution boundary value problems involving stiff operators are constructed, using the weak limits of their eigenvectors. This approach leads to a decomposition into "regular" approximation and "internal layer" approximation, which are found separately and then combined to provide an approximation to the original problem. This methodology is not complicated. Moreover, it alleviates the inherent stiffness when numerical algorithms are employed. Third, the same approach is applied to some control problems. In this case, similar results are obtained, provided additional requirements are satisfied, due to the type of control, which may drastically alter the system behavior.","abstract_has_math":false,"creators":["Salhi, Hassen"],"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":"2014-12-15T19:04:33Z","date_published":"2014-12-15T19:04:33Z","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)AAI8324634"],"render_values":[{"text":"(UMI)AAI8324634","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69258","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Salhi, Hassen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:04:33Z","10000-01-01","1983"]},{"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/2142/69258","(UMI)AAI8324634"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis examines a class of systems whose models are described by linear partial differential equations that depend on a small parameter (epsilon). First, the spectral decomposition of the so-called "stiff" operators (using the terminology of {24}) is investigated, including the convergence of their eigenvalue-eigenvector pairs as (epsilon) (--->) 0, with the objective of clarifying their singular behavior. Second, asymptotic approximation of the solution boundary value problems involving stiff operators are constructed, using the weak limits of their eigenvectors. This approach leads to a decomposition into "regular" approximation and "internal layer" approximation, which are found separately and then combined to provide an approximation to the original problem. This methodology is not complicated. Moreover, it alleviates the inherent stiffness when numerical algorithms are employed. Third, the same approach is applied to some control problems. In this case, similar results are obtained, provided additional requirements are satisfied, due to the type of control, which may drastically alter the system behavior.","Made available in DSpace on 2014-12-15T19:04:33Z (GMT). No. of bitstreams: 1 8324634.pdf: 3998129 bytes, checksum: bd19765fbd72178cc587ca7e02650b7c (MD5) Previous issue date: 1983","Embargo set by: Seth Robbins for item 69424 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","182 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983."]},{"key":"dc:title","label":"Title","values":["Analysis and Control of a Class of Stiff Linear Distributed Systems"]}]}],"canonical_facts":{"dc:creator":["Salhi, Hassen"],"dc:date":["2014-12-15T19:04:33Z","10000-01-01","1983"],"dc:description":["This thesis examines a class of systems whose models are described by linear partial differential equations that depend on a small parameter (epsilon). First, the spectral decomposition of the so-called "stiff" operators (using the terminology of {24}) is investigated, including the convergence of their eigenvalue-eigenvector pairs as (epsilon) (--->) 0, with the objective of clarifying their singular behavior. Second, asymptotic approximation of the solution boundary value problems involving stiff operators are constructed, using the weak limits of their eigenvectors. This approach leads to a decomposition into "regular" approximation and "internal layer" approximation, which are found separately and then combined to provide an approximation to the original problem. This methodology is not complicated. Moreover, it alleviates the inherent stiffness when numerical algorithms are employed. Third, the same approach is applied to some control problems. In this case, similar results are obtained, provided additional requirements are satisfied, due to the type of control, which may drastically alter the system behavior.","Made available in DSpace on 2014-12-15T19:04:33Z (GMT). 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