In this dissertation, we consider solutions of hybrid systems in which both continuous dynamics and discrete events coexists. One
of the main ingredients of our models is the two-time-scale formulation. Under broad conditions, asymptotic expansions are developed for the solutions of the systems of backward equations for switching diffusion in two classes of models, namely, fast switching systems and fast diffusion systems. To prove the validity of the asymptotic expansions, uniform error bounds are obtained.
In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has a limit. Using the limit system as a guide, our effort is devoted to deriving a sufficient condition for the stability of the original system. These results present a perspective on reduction of complexity from stability and asymptotic analysis points of view.
","abstract_html":"<p>In this dissertation, we consider solutions of hybrid systems in which both continuous dynamics and discrete events coexists. One</p> <p>of the main ingredients of our models is the two-time-scale formulation. Under broad conditions, asymptotic expansions are developed for the solutions of the systems of backward equations for switching diffusion in two classes of models, namely, fast switching systems and fast diffusion systems. To prove the validity of the asymptotic expansions, uniform error bounds are obtained.</p> <p>In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has a limit. Using the limit system as a guide, our effort is devoted to deriving a sufficient condition for the stability of the original system. These results present a perspective on reduction of complexity from stability and asymptotic analysis points of view.</p>","abstract_has_math":false,"creators":["Nguyen, Dung Tien"],"institution":null,"degree_name":"Ph.D.","degree_level":"Open Access Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["GEORGE G. YIN"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T05:58:57Z","subjects":["asymptotic expansion","hybrid systems","singular system","stability","system of backward equation","two-time scale","Applied Mathematics","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wayne.edu/oa_dissertations/324","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["GEORGE G. YIN"]},{"key":"dc:creator","label":"Author","values":["Nguyen, Dung Tien"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2011-01-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["asymptotic expansion","hybrid systems","singular system","stability","system of backward equation","two-time scale","Applied Mathematics","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wayne.edu/oa_dissertations/324"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this dissertation, we consider solutions of hybrid systems in which both continuous dynamics and discrete events coexists. One
of the main ingredients of our models is the two-time-scale formulation. Under broad conditions, asymptotic expansions are developed for the solutions of the systems of backward equations for switching diffusion in two classes of models, namely, fast switching systems and fast diffusion systems. To prove the validity of the asymptotic expansions, uniform error bounds are obtained.
In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has a limit. Using the limit system as a guide, our effort is devoted to deriving a sufficient condition for the stability of the original system. These results present a perspective on reduction of complexity from stability and asymptotic analysis points of view.
"]},{"key":"dc:title","label":"Title","values":["Asymptotic expansions and stability of hybrid systems with two-time scales"]}]}],"canonical_facts":{"dc:contributor":["GEORGE G. YIN"],"dc:creator":["Nguyen, Dung Tien"],"dc:date.available":["2011-01-01T08:00:00Z"],"dc:description.abstract":["In this dissertation, we consider solutions of hybrid systems in which both continuous dynamics and discrete events coexists. One
of the main ingredients of our models is the two-time-scale formulation. Under broad conditions, asymptotic expansions are developed for the solutions of the systems of backward equations for switching diffusion in two classes of models, namely, fast switching systems and fast diffusion systems. To prove the validity of the asymptotic expansions, uniform error bounds are obtained.
In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has a limit. Using the limit system as a guide, our effort is devoted to deriving a sufficient condition for the stability of the original system. These results present a perspective on reduction of complexity from stability and asymptotic analysis points of view.
"],"dc:identifier":["https://digitalcommons.wayne.edu/oa_dissertations/324"],"dc:subject":["asymptotic expansion","hybrid systems","singular system","stability","system of backward equation","two-time scale","Applied Mathematics","Mathematics"],"dc:title":["Asymptotic expansions and stability of hybrid systems with two-time scales"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:58:57Z"}