{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1686"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1686","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Controllability, Observability and Realizability","abstract":"In this research project, we analyze three important concepts of the control theory, including controllability, observability and realizability. In particular, we analyze the theory of and solutions to linear time systems, continuous and discrete time systems, time-varying systems, and first-order matrix Sylvester systems. Examples and sample computed calculations are provided for both uncontrolled and controlled systems. We also develop a new method for computing the approximate values of matrix exponentials, and use this to estimate solutions to initial value problems.","abstract_html":"In this research project, we analyze three important concepts of the control theory, including controllability, observability and realizability. In particular, we analyze the theory of and solutions to linear time systems, continuous and discrete time systems, time-varying systems, and first-order matrix Sylvester systems. Examples and sample computed calculations are provided for both uncontrolled and controlled systems. We also develop a new method for computing the approximate values of matrix exponentials, and use this to estimate solutions to initial value problems.","abstract_has_math":false,"creators":["Smith, Inna N."],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Scott N. Kersey","Yan Wu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-12-01T08:00:00Z","date_published":"2005-12-01T08:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Control theory","Controllability","Observability","Realizability","Duality","Transfer function","Matrix exponential function","Fundamental matrix solution","Sylvester systems","Functional analysis","Operator theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/686","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Scott N. 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In particular, we analyze the theory of and solutions to linear time systems, continuous and discrete time systems, time-varying systems, and first-order matrix Sylvester systems. Examples and sample computed calculations are provided for both uncontrolled and controlled systems. We also develop a new method for computing the approximate values of matrix exponentials, and use this to estimate solutions to initial value problems."]},{"key":"dc:title","label":"Title","values":["Controllability, Observability and Realizability"]}]}],"canonical_facts":{"dc:contributor":["Scott N. Kersey","Yan Wu"],"dc:creator":["Smith, Inna N."],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["In this research project, we analyze three important concepts of the control theory, including controllability, observability and realizability. In particular, we analyze the theory of and solutions to linear time systems, continuous and discrete time systems, time-varying systems, and first-order matrix Sylvester systems. Examples and sample computed calculations are provided for both uncontrolled and controlled systems. We also develop a new method for computing the approximate values of matrix exponentials, and use this to estimate solutions to initial value problems."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/686"],"dc:subject":["ETD","Control theory","Controllability","Observability","Realizability","Duality","Transfer function","Matrix exponential function","Fundamental matrix solution","Sylvester systems","Functional analysis","Operator theory"],"dc:title":["Controllability, Observability and Realizability"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}