{"id":{"repo_id":"exeter","oai_identifier":"oai:figshare.com:article/31231519"},"canonical_url":"https://search.dev.ndltd.org/etd/exeter/oai:figshare.com:article/31231519","repository":{"repo_id":"exeter","name":"University of Exeter","base_url":"https://api.figshare.com/v2/oai"},"display":{"title":"Linear Discrete-time Dissipative Systems","abstract":"Dissipativity is an important unifying concept across systems and control theory, being a generalisation of the concept of energy and the stability methods of Lyapunov. This thesis concerns discrete-time dissipative systems, and its main goal is to present versions of the discrete-time positive real and discrete-time bounded real lemmas that do not require the assumptions of controllability and observability, and in fact require no assumptions at all. The optimal control problem associated with passive systems is solved, likewise for non-expansive systems. A brief history of dissipativity is discussed, with particular highlighting of the context of the Cold War and the choice of names for concepts in Systems and Control theory.<p></p>","abstract_html":"Dissipativity is an important unifying concept across systems and control theory, being a generalisation of the concept of energy and the stability methods of Lyapunov. This thesis concerns discrete-time dissipative systems, and its main goal is to present versions of the discrete-time positive real and discrete-time bounded real lemmas that do not require the assumptions of controllability and observability, and in fact require no assumptions at all. The optimal control problem associated with passive systems is solved, likewise for non-expansive systems. A brief history of dissipativity is discussed, with particular highlighting of the context of the Cold War and the choice of names for concepts in Systems and Control theory.&lt;p&gt;&lt;/p&gt;","abstract_has_math":false,"creators":["Edward Branford (21038150)"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-13T00:00:00Z","date_published":"2025-08-13T00:00:00Z","updated_at":"2026-07-27T19:34:37Z","subjects":["Linear systems","dissipative systems","passive systems","discrete-time positive real lemma","discrete-time bounded real lemma","optimal control","time-invariant systems"],"languages":[],"rights":["All rights reserved","Open Access after 2027-07-12"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10779/exe.31231519.v1"],"render_values":[{"text":"10779/exe.31231519.v1","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Edward Branford (21038150)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-08-13T00:00:00Z"]},{"key":"dc:relation","label":"Dc Relation","values":["https://figshare.com/articles/thesis/Linear_Discrete-time_Dissipative_Systems/31231519"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Linear systems","dissipative systems","passive systems","discrete-time positive real lemma","discrete-time bounded real lemma","optimal control","time-invariant systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["All rights reserved","Open Access after 2027-07-12"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10779/exe.31231519.v1"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dissipativity is an important unifying concept across systems and control theory, being a generalisation of the concept of energy and the stability methods of Lyapunov. This thesis concerns discrete-time dissipative systems, and its main goal is to present versions of the discrete-time positive real and discrete-time bounded real lemmas that do not require the assumptions of controllability and observability, and in fact require no assumptions at all. The optimal control problem associated with passive systems is solved, likewise for non-expansive systems. A brief history of dissipativity is discussed, with particular highlighting of the context of the Cold War and the choice of names for concepts in Systems and Control theory.<p></p>"]},{"key":"dc:title","label":"Title","values":["Linear Discrete-time Dissipative Systems"]}]}],"canonical_facts":{"dc:creator":["Edward Branford (21038150)"],"dc:date":["2025-08-13T00:00:00Z"],"dc:description":["Dissipativity is an important unifying concept across systems and control theory, being a generalisation of the concept of energy and the stability methods of Lyapunov. This thesis concerns discrete-time dissipative systems, and its main goal is to present versions of the discrete-time positive real and discrete-time bounded real lemmas that do not require the assumptions of controllability and observability, and in fact require no assumptions at all. The optimal control problem associated with passive systems is solved, likewise for non-expansive systems. A brief history of dissipativity is discussed, with particular highlighting of the context of the Cold War and the choice of names for concepts in Systems and Control theory.<p></p>"],"dc:identifier":["10779/exe.31231519.v1"],"dc:relation":["https://figshare.com/articles/thesis/Linear_Discrete-time_Dissipative_Systems/31231519"],"dc:rights":["All rights reserved","Open Access after 2027-07-12"],"dc:subject":["Linear systems","dissipative systems","passive systems","discrete-time positive real lemma","discrete-time bounded real lemma","optimal control","time-invariant systems"],"dc:title":["Linear Discrete-time Dissipative Systems"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T19:34:37Z"}